Answers
y² = 64 -(x -2)²
y² = 64 -(x² -4x +4)
y² = -x² +4x +60
The answer is ...
D. y² = -x² +4x +60
Related Questions
Given the following sets:
A={ 2, 4, 6, 8, 10}
B={ 3, 5, 7, 9}
C={ 2, 3, 5, 7}
N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Match the following Unions and intersections to the correct set.
1.
What is A U C?
2.
What is A ∩ B?
3.
What is A ∩ N?
4.
What is B ∩ N?
5.
What is B U C?
{2, 3, 4, 5, 6, 7, 8, 10}
{2, 3, 5, 7, 9}
{ }
{3, 5, 7, 9}
{2, 4, 6, 8, 10}
Answers
B = {3, 5, 7, 9}
C = {2, 3, 5, 7}
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
1. A ∪ C = {2; 3; 4; 5; 6; 7; 8; 10}
2. A ∩ B = { } =Ø
3. A ∩ N = {2; 4; 6; 8; 10} = A
4. B ∩ N = {3; 5; 7; 9} =B
5. B ∪ C = {2; 3; 5; 7; 9}
Cross section of a metal ingot is a trapezoid the cross section has an area of 39 square cm the top base of the cross section is 12 CM the length of the bottom base is 2 cm greater than the top base how tall is the Metal Ingot explain
Answers
A = (1/2)(b₁ +b₂)×h
Fill in the given information and solve for h.
39 cm² = (1/2)(12 cm +(12 cm +2 cm))×h
39 cm²/(13 cm) = h = 3 cm
The height of the metal ingot is 3 cm.
On a coordinate graph, points F (4,1), G (4,-1), H (-7,1) and J (-7,-1) are the vertices of a rectangle. What is the area of the rectangle?
PLEASE EXPLAIN HOW YOU GOT THE ANSWER!!!!
Answers
The area is 11*2 = 22 square units.
hey can you please help me posted picture of question
Answers
Solution is shown below
[tex]y= 4 x^{3} \\ \\ \frac{y}{4} = x^{3} \\ \\ \sqrt[3]{\frac{y}{4}} =x \\ \\ f^{-1}(y)= \sqrt[3]{\frac{y}{4}} \\ \\ f^{-1}(x)= \sqrt[3]{\frac{x}{4}} \\ \\ y^{-1}= \sqrt[3]{\frac{x}{4}} [/tex]
Use the given information to find the indicated probability. a and b are mutually exclusive. p(a) = .8, p(b) = .1. find p((a ∪ b)').
Answers
[tex]\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)=0.8+0.1=0.9[/tex]
Then [tex]\mathbb P((A\cup B)')=1-\mathbb P(A\cup B)=0.1[/tex].
A neighbor needs to put up a square fence around her garden to keep the deer out. If the area is 500 square feet, how much fence does she need to buy, rounded to the nearest tenth of a foot? Show your work.
Answers
And since it’s a square the length and width is the same amount
So width=length=L
500 ft^2=L*L=L^2
Square root both sides
Sqrt(500 ft^2) =L= 22.36067977
The neighbor needs to buy approximately 89.6 feet of fencing to surround her 500 square feet garden, which is a square. This is calculated by taking the square root of the area to find the length of one side and then multiplying by four to get the perimeter.
To determine how much fence the neighbor needs to buy to surround her square garden, we need to calculate the perimeter of the square. The area of a square is given by the formula Area = side × side or Area = side². Since the area is 500 square feet, we first find the length of one side of the square by taking the square root of the area:
Side = √Area = √500 ft²
The square root of 500 is approximately 22.4 feet. Now, we calculate the perimeter, which is the sum of all four sides of the square:
Perimeter = 4 × side = 4 × 22.4 ft = 89.6 ft
Rounded to the nearest tenth of a foot, the neighbor needs to buy approximately 89.6 feet of fencing to surround her garden.
What is the quadratic function with the given vertex and through the given point? Write the equation of the parabola in vertex form and describe how the function was transformed from the parent function y = x2.
vertex (0, 0), point (−2, 2)
Answers
y = A(x - h)² + k
Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
The coefficient A may be found when you have another point of the quadratic function.
2) Therefore, being the vertex (0,0), h = 0 and k = 0, and the equation is
y = Ax²
3) Replacing the coordinates of the point (-2,2) into the equation you get:
2 = A (-2)² ⇒ A = 2/4 = 1/2
4) The resulting equation is y = (1/2)x² ← answer
Since, the system is giving me an error, I had to put the second part of the answer in a separate file. Please, see the attached pdf file.
The quadratic function with vertex (0, 0) and passing through the point (-2, 2) is y = 0.5x^2. This is a transformation of the parent quadratic function y = x^2 with a vertical stretch by a factor of 0.5.
Explanation:The quadratic function with the given vertex (0, 0) and going through the point (-2, 2) can be written in the form of the vertex form of a quadratic function i.e. y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex given is (0,0), the function becomes y = ax².
Now, to find the value of 'a', we can substitute the x and y coordinates of the given point (-2,2) into the equation. So, 2 = a(-2)², this simplifies to 2 = 4a. Solving for 'a', we get a = 0.5. So, the function is y = 0.5x².
This function is a transformation of the parent function y=x². The 0.5 in front of x² means that the graph of the function stretches vertically by a factor of 0.5. Thus, the parabola opens upwards and is narrower than the parent function.
Learn more about Quadratic Function here:https://brainly.com/question/35505962
#SPJ11
Help Please..
Arrange from smallest to largest
0.2 , 0.06, 0.602, 0.026, 0.21
Answers
Q and R are not mutually exclusive events. p (q) = 3/5 p(r) = 1/3 and p ( q and r)= 1/5 find P(Q or R).
Answers
[tex]\mathbb P(Q\cup R)=\mathbb P(Q)+\mathbb P(R)-\mathbb P(Q\cap R)[/tex]
which means
[tex]\mathbb P(Q\text{ or }R)=\dfrac35+\dfrac13-\dfrac15=\dfrac{11}{15}[/tex]
The answer to this item is 23/32.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
Given that the events are not mutually exclusive the union of the probability of the events is calculated through the equation,
P(Q or R) = P(Q) + P(R) - P(Q and R)
Substituting the known values,
P(Q or R) = 3/5 + 1/3 - 1/5
Simplifying,
P(Q or R) = 11/15
Hence the answer to this item is 23/32.
Learn more about probability click;
https://brainly.com/question/32117953
#SPJ1
Find the greatest common divisor of 100 and 254, using • prime factorization- • euclidean algorithm-
Answers
[tex]100=10^2=2^2\cdot5^2[/tex]
[tex]254=2\cdot127[/tex]
of which the only common factor is a single power of 2, so [tex]\mathrm{gcd}(100,254)=2[/tex].
Via the Euclidean algorithm:
[tex]254=2\cdot100+54[/tex]
[tex]100=1\cdot54+46[/tex]
[tex]54=1\cdot46+8[/tex]
[tex]46=5\cdot8+6[/tex]
[tex]8=1\cdot6+2[/tex]
[tex]6=3\cdot2+0[/tex]
which means [tex]\mathrm{gcd}(100,254)=2[/tex], as expected.
The Greatest Common Divisor (GCD) of 100 and 254 can be found using Prime Factorization and the Euclidean Algorithm. Both methods produce a GCD of 2.
Explanation:The student is asking for how to find the Greatest Common Divisor (GCD) of 100 and 254 using two different methods: Prime Factorization and the Euclidean Algorithm.
Prime Factorization: Start by writing down each number's prime factors. The prime factors for 100 are 2, 2, 5, 5 and the prime factors for 254 are 2, 127. The GCD is the product of the smallest power of each common prime number. In this case, the only common prime number is 2, so the GCD by prime factorization is 2.Euclidean Algorithm: This method begins with the larger number (254) and divides it by the smaller one (100). Write down the remainder (54). Then, divide the smaller number (100) by the remainder from the last step (54) to get a new remainder (46). The process is repeated until there is no remainder. The last non-zero remainder serves as the GCD. In this case, the process would continue as follows: 54 divided by 46 equals 1 remainder 8, then 46 divided by 8 equals 5 remainder 6, then 8 divided by 6 equals 1 remainder 2, then 6 divided by 2 equals 3, no remainder. Therefore, the GCD by Euclidean Algorithm is also 2.Learn more about Greatest Common Divisor here:https://brainly.com/question/23270841
#SPJ11
evaluate the following expressions 7/8 ×5/7 =
Answers
Anyone care to help with this please
Answers
For the first equation, only one choice has a midline y = 4, which is h(x).
For the second equation, the first and fifth choices have midline y = 8, but the frequency of 2 only fits the fifth choice: q(x).
For the third equation, the midline of y = 1 only fits g(x).
The fourth equation has midline y = 2 and frequency of 4, which only fits the last choice, r(x).
the angle of the first hill of a roller coaster is 55 degrees. if the length of the track from the beginning of the ascent to the highest point is 98 feet, what is the height if the roller coaster when it reaches the top of the first hill?
Answers
sin θ=opposite/hypotenuse
θ=55°
opposite=h
hypotenuse=98 ft
thus the height will be:
sin 55=h/98
solving for h we get:
h=98×sin55
h=80.28 ft
Thus the height is 80.28 ft
Simplify the expression (a^2b^5c^3)^4(a^3b^3)^3(a^2c)^2
Answers
[tex]( a^{2} b^{5} c^{3} )^{4} ( a^{3} b^{3} )^{3} ( a^{2} c )^{2} \\ \\ =( a^{8} b^{20} c^{12} )( a^{9} b^{9} )( a^{4} c^{2} ) \\ \\ = a^{(8+9+4)} b^{(20+9)} c^{(12+2)} \\ \\ = a^{21} b^{29} c^{14} [/tex]
The price of an item has risen to $276 today. Yesterday it was $115. Find the percentage increase.
Answers
276-115=131
131 divided by 276 = 0.47
0.47% increase
The student's question asked for finding the percentage increase in an item's price. This can be calculated by subtracting the initial price from the final price, dividing that difference by the initial price, and then multiplying the result by 100. In this case, the price of the item has increased by 140% from yesterday to today.
Explanation:To find the percentage increase of the price of an item, we subtract the initial price from the final price, then divide that number by the initial price, finally multiply that result by 100 to obtain the percentage. In this case, the initial price of the item was $115, and the final price is $276.
Here's how the calculation works:
Subtract the initial price from the final price: $276 - $115 = $161. Divide the difference by the initial price: $161 / $115 ≈ 1.4. Multiply the result by 100 to get the percentage increase: 1.4 * 100 = 140%.
Therefore, the price of the item has increased by 140% from yesterday to today.
Learn more about Percentage Increase here:https://brainly.com/question/20818421
#SPJ2
Can you please help me with this math problem
Answers
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).
Area Trapezoid = (b1 + b2) * h / 2
b1 = 8
b2 = 12
h = 5
Area Trapezoid = (8 + 12 ) * 5 / 2
Area Trapezoid = 20 * 5/2
Area = 50 square feet.
The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5 = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.
Determine the number of solutions the following system of equations will have: 1/3 y - 5 = 2x y = 15 + 6x
Answers
1/3 y - 5 = 2x
y = 15 + 6x
The equations are linearly dependent, that is, there is a scalar that allows us to write an equation as a linear combination of the other.
We multiply the equation (1) by a scalar, which will be 3:
3 * (1/3 y - 5) = 3 * (2x)
Rewriting:
y-15 = 6x
y = 15 + 6x
Answer:
Therefore, if there is a solution, then there are infinite solutions.
A college cafeteria pays student cashiers $10.20 per hour. Cashiers earn an additional $1.30 per hour for each hour worked over 35 hours per week. A cashier worked 40 hours one week and 38 hours the second week. How much did this cashier earn in this two-week period?
Answers
Total Earning = 40 x $10.20 + (40 - 35) x $1.30 = $414.50
Second Week: 38 hours
Total Earning = 40 x $10.20 + (40 - 38) x $1.30 = $410.60
Total for the two weeks = $414.50 + $410.60 = $825.10
Answer: $825.10
Answer:
$806
Step-by-step explanation:
The regular earning of a cashier = $10.20 per hour
over 35 hours per week he gets = $10.20 + $1.30 per hour
= $11.50 per hour
He worked 40 hours in first week and 38 hours the second week.
His earnings in first week = (35 × 10.20) + (5 × 11.50)
= $357 + $57.5
= $414.50
His earnings in second week = (35 × 10.20) + (3 × 11.50)
= $357 + $34.50
= $391.50
His total earnings in this two weeks = $391.50 + $414.50
= $806
His total earning was $806.
HELP FAST!! What is the volume of a right rectangular prism with a base that measures 4 in by 6 in. and a height of 7 in? A) 17 in.3. B) 51 in.3. C) 84 in.3. D) 168 in.3.
Answers
What you need to do first is multiply 6 and 4 together. Once you've done that, you now have 24. You now need to multiply 24 by 7 to get 168. Now you have 168 in³ for your Volume.
I hope this helps!
Answer:
d
Step-by-step explanation:
Solve the systems x ≡ 1 (mod 2), x ≡ 2 (mod 3). x ≡ 2 (mod 5), 2x ≡ 3 (mod 7), 3x ≡ 4 (mod 11). x ≡ 31 (mod 41), x ≡ 59 (mod 26).
Answers
We know that '[tex]x=1(mod 2)[/tex]' means 2 divides '[tex]x-1[/tex]'. Keep in mind I can't add a three line "equality" symbol in Brainly...
The previous can be written with this statement:
[tex]x-1=2k[/tex]
In which '[tex]k[/tex]' is any integer.
From the previous equation is very easy to see that '[tex]x=2k+1[/tex]'.
We write the remaining congruence modulo relations as equations and solve for them in similar fashion:
[tex] x_{1}-2=3k [/tex]
[tex] x_{2}-2=5k [/tex]
[tex] 2x_{3}-3=7k [/tex]
[tex] 3x_{4}-4=11k [/tex]
[tex] x_{5}-31=41k [/tex]
[tex] x_{6}-59=26k [/tex]
Now we solve for the x's, remember, k is any integer!
[tex] x_{1} =3k+2[/tex]
[tex] x_{2} =5k+2[/tex]
[tex] x_{3} = \frac{7k+3}{2} [/tex]
[tex] x_{4} = \frac{11k+4}{3} [/tex]
[tex] x_{5} =41k+31[/tex]
[tex] x_{6} =26k+59[/tex]
Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ
Answers
ANSWER
Component form:
[tex]\binom{ - 16}{2} [/tex]
2. Magnitude
[tex]2\sqrt{65} [/tex]
EXPLANATION
Given that P = (-5, 5) and Q = (-13, 6),
Vector PQ
[tex] = \binom{ - 13}{6} - \binom{ - 5}{5} [/tex]
[tex] = \binom{ - 13 + 5}{6 - 5} [/tex]
[tex] = \binom{ - 8}{1} [/tex]
2 vector PQ
[tex] = 2 \binom{ - 8}{1} [/tex]
[tex] = \binom{ - 16}{2} [/tex]
This is the component form.
The magnitude is given by
[tex] = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex] = \sqrt{ {( - 16)}^{2} + {2}^{2} } [/tex]
[tex] = \sqrt{256 + 4} [/tex]
[tex] = \sqrt{260} [/tex]
[tex] = 2\sqrt{65} [/tex]
Is a cubic inch is the space taken by a cube whose sides are 1 inch long?
Answers
A cubic inch is the space taken by a cube that sides are 1 inch long
The answer is Yes or true
Hope this helps!
What is the height of a triangle that has an area of 60 yd squared and a base with a length of 12 yd
Answers
_______________________________________________________
The height of the triangle is: " 10 yd " .
_______________________________________________________
Explanation:
_______________________________________________________
The formula for the area, "A", of a triangle is:
→ " A = (b * h) / 2 " ;
in which: " A = area (in square units; in this case; "yd² " ;
= " 60 yd² " {given} ;
"b = base length = 12 yd" {given} ;
"h = [perpendicular] height ; for which we shall solve;
_______________________________________________________
→ A = (b * h) / 2 ;
→ Rearrange the equation to isolate "h" on one side of the equation; since we need to solve for "h" (height) ;
→ Multiply each side of the equation by "2" ;
→ 2 * A = 2 * [ (b * h) / 2 ] ;
to get:
→ 2A = b * h ;
↔ b * h = 2A ;
Divide each side of the equation by "b" ;
to isolate "h" on one side of the equation;
→ (b * h) / b = 2A / b ;
→ h = 2A / b ;
Now, plug in our given values for "A" and "b" ;
to solve for "h" ;
→ h = (2* 60 yd²) / (12 yd) ;
= (120 yd²) / (12 yd).
= 10 yd.
→ h = 10 yd.
_______________________________________________________
The answer is: " 10 yd. " .
_______________________________________________________
The height of the triangle is: " 10 yd " .
_______________________________________________________
hey can you please help me posted picture of question
Answers
it has a slope equal to 1 and passes through the origin. All the other linear functions are derived from this parent function.
So, the correct answer to this question is option B
6. Alice Correa bought three yards of cloth to make a dress. The cloth was on sale for $1.93 per yard. How much did Alice pay for the cloth if the sales tax was 5 percent? A. $5.79 B. $2.02 C. $6.08 D. $5.82
Answers
$1.93 per yard x 3 yards = $5.79 before tax
5% sales tax means that there will be 0.05 added to the price of the product
$5.79 x 1.05 = 6.0795 = $6.08
Suppose a weather forecaster says the probability that it will rain on saturday is 2929% and the probability that it will rain on sunday is 4040%. from this information, is it possible to find the probability that it will rain on saturday or sunday (or both)? why or why not?
Answers
julie will build a rectangular pen for her dog against a barn. A wall from the barn will from one side of the pen. She has 32m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area. What will be the dimensions of julie's pen?
Answers
the answer is 8 and 16
A population of protozoa develops with a constant relative growth rate of 0.8877 per member per day. on day zero the population consists of six members. find the population size after five days. (round your answer to the nearest whole number.) p(5) = members
Answers
p(t) = 6×1.8877^t
The population size when t=5 is then
p(5) = 6×1.8877^5 ≈ 144 . . . . members
Assume that X has a normal distribution, and find the indicated probability. The mean is μ= 15.2 and the standard deviation is σ = 0.9. Find the probability that X is greater than 16.1.
Answers
Answer:0.1587
Step-by-step explanation:
z = (x-μ)/σ
mean, μ= 15.2
standard deviation, σ = 0.9
To find the probability that x is greater than 16.1,
x = 16.1
z = (16.1-15.2)/0.9
= 1
Looking at the normal distribution table, the area covered by 0 to 1
=0.8413
Therefore, the probability that x is greater than 16.1, = 11- probability that x = 16.1
= 1-0.8413
= 0.1587
Which stem-and-leaf plot represents the data? 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 5, 5, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 6, a stem value of 2, a stem value of 3 with a leaf value of 0, and a stem value of 4 with a leaf value of 8, 8, 8. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, 6, 6, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15 A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, a stem value of 2 with a leaf value of 9, a stem value of 3 with a leaf value of 0, a stem value of 4 with a leaf value of 8, 8, 8, a stem value of 5, and a stem value of 6 with a leaf value of 3. Key: 1|5 means 15
Answers
Here is the data in order and the Stem and Leaf plot created:
15, 15, 15, 16, 16, 29, 30, 48, 48, 48, 63
Stem|Leaf
1 | 5 5 5 6 6
2 | 9
3 | 0
4 | 8 8 8
5 |
6 | 3
Key:1|5 = 15
Options: A
A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 5, 5, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, A stem value of 5A stem value of 6 with a leaf value of 3.Key: 1|5 means 15
Options: B
A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 6, A stem value of 2, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8.Key: 1|5 means 15
Options: C
A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, A stem value of 5, and a stem value of 6 with a leaf value of 3.Key: 1|5 means 15
Options: D
A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8, A stem value of 5A stem value of 6 with a leaf value of 3.Key: 1|5 means 15
Answer:
Options: D
A stem-and-leaf plot with a stem value of 1 with a leaf value of 5, 5, 5, 6, 6, A stem value of 2 with a leaf value of 9, A stem value of 3 with a leaf value of 0, A stem value of 4 with a leaf value of 8, 8, 8, A stem value of 5A stem value of 6 with a leaf value of 3.Key: 1|5 means 15
Step-by-step explanation:
Given: 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48
To plot a stem and leaf plot, first rearrange the observations in ascending order: 15, 15, 15, 16, 16, 29, 30, 48, 48, 48 , 63
Next, is to get the range of values
Low: 15
High = 63
Next, is to identify the stems
Using the range of 15 to 63, we need stems of 1, 2, 3, 4, 5 and 6
In tabular form, the stems are:
Stems ||
1 ||
2 ||
3 ||
4 ||
5 ||
6 ||
Next, is to fill in the leafs
Stem || Leaf
1 || 5 5 5 6 6
2 || 9
3 || 0
4 || 8 8 8
5 ||
6 || 3
Lastly, we write out our observations
1. The stem Value 1 has leaf values 5,5,5,6,6
2. The stem Value 2 has a leaf value 9
3. The stem Value 3 has a leaf value 0
4. The stem Value 4 has leaf Values 8,8,8
5. The stem Value 5 has no leaf
6. The stem Value 6 has leaf value 3
Comparing the observation with the options, option D represents the stem-and-leaf plot representation of 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48