which expression represents a circle with a center at (2, -8) and a radius of 11?
Answer:
(x - 2)² + (y + 8)² = 121
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (2, - 8) and r = 11, hence
(x - 2)² + (y + 8)² = 121
The equation [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex] represents a circle with a center at (2, -8) and a radius of 11. This is derived from the general circle equation [tex]\((x - h)^2 + (y - k)^2 = r^2\).[/tex]
The correct equation representing a circle with a center at (2, -8) and a radius of 11 is option (b) [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex].
The general equation of a circle is [tex]\((x - h)^2 + (y - k)^2 = r^2\)[/tex], where (h, k) is the center and r is the radius.
In option (b), [tex]\((x-2)^2 + (y + 8)^2 = 121\)[/tex], the values match the given center (2, -8) and radius of 11. The squared terms with (x-2) and (y+8) are in the correct form, and the radius squared [tex](\(11^2 = 121\))[/tex] is on the right side.
Options (a), (c), and (d) do not represent the given circle because they have incorrect signs, centers, or radius values. Therefore, the correct equation is option (b).
Gail bought 18 buttons to put on the shirts she makes she uses five buttons for each shirt how many shirts can still make with the buttons she Bought
18/5 is 3.6. You must always round down because you would be using more buttons if you did. So round down 3.6 to get 3.
can someone please help n fast
Answer: 1. D) Exponents 2. A) Addition and subtraction from left to right
Step-by-step explanation: PEMDAS will help you to understand! Remember, first, its parentheses, then exponents (Answer for Question 1), then multiply and divide from left to right, then add and subtract from left to right (Answer for Question 2).
Hope this helped!
Plz mark brainliest!
Which is the definition of an acute triangle?
Answer:
A triangle with angles less than 90°
Step-by-step explanation:
An acute triangle is a triangle where all its interior angles are less than 90 degrees, distinguishing it from other types of triangles.
Explanation:In mathematics, an acute triangle is a type of triangle where all three of its interior angles are less than 90 degrees. This is what distinguishes it from other types of triangles such as right triangles, which have one angle of exactly 90 degrees, or obtuse triangles, where one angle is larger than 90 degrees. For example, a triangle with angles of 30, 60, and 90 degrees would be considered an acute triangle because all the angles are less than 90 degrees.
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how do you simplify 27 over 20
Answer:
1 7/20
Step-by-step explanation:
well 27/20 is 1 and 7/20
make it to a improper fraction
Answer:
1 7/20
Step-by-step explanation:
The fraction given to us (27/20) is called an improper fraction, because the numerator (top number) is greater than the denominator (bottom number).
In this case, break it down. You know that when the numerator & denominator have the same number, it will equal 1. And so change the number.
27/20 = (20 + 7)/20
20/20 = 1
7/20 is left over
1 7/20 is your answer
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Find the diagonal (d) of the base
Answer:
[tex]4\sqrt{5}\ un.[/tex]
Step-by-step explanation:
The picture shows rectangular prism with rectangular base and heigth h. The dimenssions of base rectangle are l and w.
The diagonal of reactangle with known length l and width w can be calculated using the Pythagorean theorem:
[tex]d^2=l^2+w^2,\\ \\d^2=8^2+4^2,\\ \\d^2=64+16,\\ \\d^2=80,\\ \\d=4\sqrt{5}\ un.[/tex]
Which decimal is between 0.6 and 0.7
Answer:
You can recognize that .25 is 1/4, so 0.625 is 1/4 of the way
from 0.6 to 0.7
Answer: I agree with Sauske. Sorry If I'm saying your name wrong.
Step-by-step explanation:
(45 points for a simple math problem.) Determine the percent of change between 36 and 72. (Show your work please.)
Answer:
100%
Step-by-step explanation:
Use the equation:
percent of change= [New-Old]÷Old×100100=(72-36)÷36×100
I need some help now
Answer:
Well 3/5 is .60 and 2/4 is .50 so in these regards she grew .10 more inches then her
Step-by-step explanation:
Answer:
1/10 of an inch taller
Step-by-step explanation:
3/5 2/4
12/20 10/20
2/20= 1/10
Winston can drive a total of 248 miles on Monday. He drove 70 fewer miles in the morning that he did in the afternoon. How many miles did he drive in the afternoon?
Winston drove 89 miles in the morning and 159 miles in the afternoon.
Explanation:Let's assume that Winston drove x miles in the morning. Since he drove 70 fewer miles in the morning than he did in the afternoon, he drove (x + 70) miles in the afternoon.
According to the question, he can drive a total of 248 miles in a day. So, we can write the equation: x + (x + 70) = 248
Simplifying the equation, we get: 2x + 70 = 248
Subtracting 70 from both sides, we have: 2x = 178
Finally, dividing both sides by 2, we find: x = 89
Therefore, Winston drove 89 miles in the morning and (x + 70) = 89 + 70 = 159 miles in the afternoon.
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PLEASE HELP!find the domain of the graphed function
Answer:
Domain is a set of all possible x values, so answer A is correct, as x is in [2,5].
(18 points)Hiiii guys! I will love you forever if you answer this question. And to save you some time you don’t have to show any work! Q: Patrick’s favorite shade of purple paint is made w/ 4 oounces Blue paint for every 3 ounces of red paint. Which of the following paint mixtures Will create the same shade of purple? Choose 2 answers if you would♾
It takes 4 ounces of blue paint and 3 ounces of red paint to make Patrick's favorite shade of purple.
Multiply the numbers by 2. This will not affect the proportion. Thus, the new statement will be true respect to the original one.
It takes 8 ounces of blue paint and 6 ounces of red paint to make Patrick's favorite shade of purple. That's answer choice B.
Multiply the original numbers by 5. Again, this will not affect the proportion, meaning that the statement will remain true.
It takes 20 ounces of blue paint and 15 ounces of red paint to make Patrick's favorite shade of purple. This is answer choice D.
Thus, the answers are answer choices B and D.
Two parallel lines are crossed by a transversal . What is the value of k?
Answer:
k = 60
Step-by-step explanation:
2k + 11 = 131
2k = 131 - 11
2k = 120
k = 60
I hope I helped you.
An ice cream cone that is 4cm across the top is topped with a single scoop of ice cream (spherical) that is 4cm in diameter. What is the minimum height of the cone so that when the ice cream melts, the ice cream does not overflow out of the cone? Justify your answer.
Answer:
8 cm.
Step-by-step explanation:
We have been given that an ice cream cone that is 4 cm across the top is topped with a single scoop of ice cream (spherical) that is 4 cm in diameter.
To find the minimum height of cone we will use volume of cone formula and volume of sphere as we are told that when the ice cream melts, the ice cream does not overflow out of the cone. This means that volume of sphere will be equal to volume of cone.
[tex]\text{Volume of cone}=\frac{1}{3} \pi r^2h[/tex]
[tex]\text{Volume of sphere}=\frac{4}{3} \pi r^3[/tex]
Since diameter of both cone and sphere is 4 cm, so radius will be half the diameter, that is 2 cm.
Let us substitute r=2 in both equations and equate the volumes of cone and sphere to find the height of cone.
[tex]\frac{4}{3} \pi\times 2^3=\frac{1}{3} \pi\times 2^2\times h[/tex]
[tex]\frac{4}{3} \pi\times 8=\frac{1}{3} \pi\times 4\times h[/tex]
Multiply both sides of equation by 3.
[tex]3\times \frac{4}{3} \pi\times 8=3\times \frac{1}{3} \pi\times 4\times h[/tex]
[tex]4 \pi\times 8= \pi\times 4\times h[/tex]
[tex]32 \pi= 4\pi\times h[/tex]
[tex]h=\frac{32 \pi}{4\pi}[/tex]
[tex]h=8[/tex]
Therefore, the minimum height of cone must be 8 cm.
Using the distributive property, remove the parentheses
10c^4(9-8c^2)
Also simplify
[tex]Use:\\\\a(b-c)=ab-ac\\\\a^n\cdot a^m=a^{n+m}[/tex]
[tex]10c^4(9-8c^2)=(10c^4)(9)-(10c^4)(8c^2)=90c^4-80c^{4+2}\\\\=\boxed{90c^4-80c^6}[/tex]
A lit house worker is tracking a boat that is 2.1 km south from her. She is also tracking a boat that is 3.5 km from the tower located 70 degrees east of north. To the nearest tenth of a kilometer, how far apart are the two boats?
Answer:
21.5 km
Step-by-step explanation:
We have to find the distance between two boat
We are given that
AC=2.1 km
BC=3.5 km
We have to find BC
The angle between two boat =110 degrees
Using cosine law
BC=[tex]\sqrt{(2.1)^2+(3.5)^2-2\cdot(2.1)\cdot(3.5)cos 110}[/tex]
BC=[tex]\sqrt{4.41+12.25+ 2\cdot2.1\times3.5cos 70[/tex]
BC=[tex]\sqrt{4.41+12.25+9.3051}[/tex]
BC=21.507 km
Hence, the distance between two boat is 21.5 km
The distance between the two boats can be determined using the law of cosines. Inserting the provided values into the formula yields a distance of approximately 3.9 kilometers.
Explanation:To solve this problem, we can apply the law of cosines, which states that c² = a² + b² - 2ab(cos Θ), where a and b are lengths of two sides of a triangle, c is the length of the third side, and Θ is the angle between sides a and b. Let's consider our light house worker as a starting point. The boat at 2.1 km south constitutes one side of the triangle (a = 2.1 km). The other boat, at 3.5 km 70° east of north, constitutes the second side (b = 3.5 km). The angle Θ between side a and side b is 70°. Therefore, the distance between the two boats (c) can be calculated as follows:
c² = a² + b² - 2ab(cos Θ) = (2.1 km)² + (3.5 km)² - 2 *(2.1 km)*(3.5 km) cos(70°)
Computing the above gives a distance of approximately 3.9 km.
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What integer represents saving $65?
Answer:
+$65
Step-by-step explanation:
We are asked to determine the integer that represents saving $65.
We know that savings represent a positive number. Savings stands for the amount saved by a person.
We know that loss, withdraw and spend represent negative quantities, while the savings, profit and deposit represent positive quantities, therefore, saving of $65 would be +$65.
HELP ASAP PLEASEE!! a metal alloy weighing 4 mg and containing 20% iron is melted and mixed with 12 mg of a different alloy which contains 40% iron. which percent of the resulting alloy is iron?
A)12%
B)20%
C)35%
D)55%
Answer:
35 percent
Step-by-step explanation:
To solve this problem we multiply the amount by the percent and add them up to get the total amount times the percent
amount * percent + amount * percent = total amount * percent
4 * .20 + 12 * .40 = (4+12) * x
.8 + 4.8 = 16 x
Combine like terms
5.6 = 16x
Divide by 16
5.6/16 = 16x/16
.35 =x
35 percent
what is half of 7 the whole number
Answer:
3 1/2
Step-by-step explanation:
You have to do 7 divided by 2 or 1/2 x 7
Answer:
Well it normally be 3.5
Step-by-step explanation:
You take seven and divide it by 2 (ps) if you are talking about your answer needing to be a whole answer just round up
Why do interest rates on loans tend to be lower in a weak economy than in a strong one?
Why do interest rates on loans tend to be lower in a weak economy than in a strong one?
The interest rates on loans tend to be lower in a weak economy than in a strong one because in a weak economy there is less demand for credit so the rates are lesser. In a stronger economy, the credit market demand is higher so as the demand increases the rate also increases.
Answer:
C
Step-by-step explanation:
took test
Solve the problems below. Please answer with completely simplified exact value(s) or expression(s).
a)
In ΔABC, AC = BC, CD⊥AB with D∈AB, AB = 4 in, and CD = 3 in. Find AC.
b)
Given: ΔABC, AB = BC = AC = a. Find: The area of ΔABC
Answer:
a) AC = [tex]\sqrt{13}[/tex]
b) Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]
Step-by-step explanation:
a) From question,
AC = BC, CD⊥AB
Now in ΔCAD and ΔCBD
AC=BC, ∠A = ∠B and AD=BD (because in isosceles triangle perpendicular bisects the side).
then, from SAS potulates
ΔCAD≅ΔCBD
So,
AD = [tex]\frac{AB}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 in
From Pythagorean theorem in ΔADC
[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex]
[tex]AC^{2}[/tex] = [tex]2^{2}[/tex] + [tex]3^{2}[/tex]
[tex]AC^{2}[/tex] = 4 + 9 = 13
AC = [tex]\sqrt{13}[/tex]
b) In given ΔABC,
AB = BC = AC = a, means ΔABC is a equilateral triangle.
So, area of equilateral triangle is
Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]side^{2}[/tex]
side = a
then,
Area = [tex]\frac{\sqrt 3}{4}[/tex] × [tex]a^{2}[/tex]
Answer:
a) √7
Step-by-step explanation:
Which function is undefined for x = 0? y=3√x-2 y=√x-2 y=3√x+2 y=√x=2
For this case, we have to:
By definition, we know:
The domain of [tex]f (x) = \sqrt [3] {x}[/tex] is given by all real numbers.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. In the same way, its domain will be given by the real numbers, independently of the sign of the term inside the root. Thus, it will always be defined.
So, we have:
[tex]y = \sqrt [3] {x-2}[/tex] with[tex]x = 0[/tex]: [tex]y = \sqrt [3] {- 2}[/tex] is defined.
[tex]y = \sqrt [3] {x+2}[/tex]with [tex]x = 0:\ y = \sqrt [3] {2}[/tex] is also defined.
[tex]f (x) = \sqrt {x}[/tex]has a domain from 0 to ∞.
Adding or removing numbers to the variable within the root implies a translation of the function vertically or horizontally. For it to be defined, the term within the root must be positive.
Thus, we observe that:
[tex]y = \sqrt {x-2}[/tex] is not defined, the term inside the root is negative when[tex]x = 0[/tex].
While [tex]y = \sqrt {x+2}[/tex] if it is defined for [tex]x = 0[/tex].
Answer:
[tex]y = \sqrt {x-2}[/tex]
Option b
Answer:
B on EDGE
Step-by-step explanation:
Find the probability of this event. Enter each answer as a fraction in simplest form, as a decimal, and as a percent. You draw one card at random from a shuffled deck of 52 playing cards. The deck has four 13−card suits (diamonds, hearts, clubs, spades). The card is a heart or a spade.
The probability expressed as a fraction is ____
The probability expressed as a decimal is ____
.
The probability expressed as a percent is_____
The length of a rectangle is 8cm greater than its width. Find the dimensions of the rectangle if it’s area is a 105cm(2)
length = area/width
l = 105/7 = 8
The length of the rectangle is 15.
The following function represents the value of a house, in dollars, after x years:
f(x) = 242,000(1.04)x
What does 1.04 represent?
The present value of the house
The value of the house after x years
The increase in the value of the house per year, which is 4%
The value of the house after x years, which will be 4% of the present value
Answer:
the 1.04 represents the increase in the house value each year, which is 4%
Answer:
The correct option is 3.
Step-by-step explanation:
The general exponential growth model is
[tex]y=a(1+r)^x[/tex] .... (1)
where, a is the initial value, r is growth rate per period and x is number of periods. Here (1+r) is growth factor.
The given function is
[tex]f(x)=242,000(1.04)^x[/tex]
It can be written as
[tex]f(x)=242,000(1+0.04)^x[/tex] .... (2)
From (1) and (2) we get
[tex]r=0.04=4\%[/tex]
In the given function 1.04 is growth factor. It means it represents increase in the value of the house per year which is 4%.
Therefore the correct option is 3.
justin starts a bank account with $85 in his savings,and he puts in an additional 15 dollars a month towards his savings
Answer:
y = 15x + 85
Step-by-step explanation:
Let:
x = amount of months ; y = total amount
The constant is 85, meaning that this number will not change (for he would have at least 85 no matter how much time has passed).
15 is next to a variable, for depending on the amount of time passed, you will add a certain amount of "15" to the answer.
y is your total, and is also a variable, because it also depends on the amount of time that passes.
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m<KGH=x+161,m<FGK=x+41,and m<FGH=180° Find x
Answer: x = -11 ∠FGK = 30° ∠KGH = 150°
Step-by-step explanation:
∠FGK + ∠KGH = ∠FGH Segment Addition Postulate
x + 41 + x + 161 = 180 Substitution
2x + 202 = 180 Simplify (added like terms)
2x = -22 Subtraction Property of Equality
x = -11 Division Property of Equality
∠FGK = x + 41 = (-11) + 41 = 30
∠KGH = x + 161 = (-11) + 161 = 150
there is $3080 in the math department fund. They need to deposit enough money in the fund to pay for a shipment work $2800, and still have $500 left for future shipments. Write an inequality to describe (d), the amount of money that needs to be deposited?
Answer:
3080+d > = 3300
Step-by-step explanation:
The first question to ask is how much money do they need in the fund?
They need the shipment costs plus the future shipment costs
2800+500 = 3300
They have 3080
Let d = how much they need to deposit
How much they have plus how much they need to deposit must be greater than or equal to how much they need.
3080+d > = 3300
fifty subtracted from a number equals eighty. find the number
Answer: hope this helps. it's 130.
Identify which equations have one solution, infinitely many solutions, or no solution.
Let's label them 1-6, for convenience.
1. 1 solution (a positive # of ys equaling a positive constant)
2. Infinitely many solutions (You get 0=0 if you completely simplify)
3. No solution (take out the 3z's; 2.5 doesn't equal 3.2)
4. Infinitely many solutions (take out the 3/4 x; 1.1+2 = 3.1)
5. No solution (take out the 4.5r; 0 doesn't equal 3.2)
6. 1 solution (x = 3 1/2)
Answer:
1) [tex]\frac{1}{2}y+\frac{32}{10}y=20[/tex] One solution
2)[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z[/tex] Infinite Number of Solutions
3) [tex]3z+2.5=3.2+3z[/tex] No solution.
4) [tex]1.1+\frac{3}{4}x+2=3.1+\frac{3}{4}x[/tex] Infinitely Many Solutions
5) [tex]4.5r=3.2+4.5r[/tex] No solution
6) [tex]2x+4=3x+\frac{1}{2}[/tex] One solution
Step-by-step explanation:
Equations may have exactly one solution, uncountable solutions or even no possible solution when the solution is a contradiction and this solution is never true.
1) [tex]\frac{1}{2}y+\frac{32}{10}y=20[/tex] One solution Let's prove it by solving it:
[tex]\frac{1}{2}y+\frac{32}{10}y=20\Rightarrow \frac{37}{10}y=20\Rightarrow 10*\frac{37}{10}y=20*10\\37y=200\Rightarrow \frac{37}{37}y=\frac{200}{37}\Rightarrow y=\frac{200}{37}\Rightarrow S=\left \{ \frac{200}{37} \right \}[/tex]
2)[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z[/tex] Infinite Number of Solutions because infinitely many solutions satisfies for z.
[tex]\frac{15}{2}+2z-\frac{1}{4}=4z+\frac{29}{4}-2z\\\frac{29}{4}+2z=\frac{29}{4}+2z[/tex]
3) [tex]3z+2.5=3.2+3z[/tex] No solution. There's no way to add 2.5 to 3z and have the same amount as adding 3.2 to 3z. This is contradiction. This is a false equality.
4) [tex]1.1+\frac{3}{4}x+2=3.1+\frac{3}{4}x[/tex] Infinitely many solutions. This equation has infinitely many solutions since the left side is equal to the right side, any value plugged in x may result in many solutions.
5) [tex]4.5r=3.2+4.5r[/tex] No solution Similarly, again. There's no way of adding 3.2 to 4.5r being equal to 4.5r. Another contradiction. This is a false equality.
6) [tex]2x+4=3x+\frac{1}{2}[/tex] One solution
[tex]2x+4=3x+\frac{1}{2}\\2x+4-2x=3x+\frac{1}{2}-2x\\4=x+\frac{1}{2}\\4-\frac{1}{2}=x\Rightarrow x=\frac{7}{2}\Rightarrow S=\left \{ \frac{7}{2} \right \}[/tex]
Since we can see on the left side different expressions than on the right side. All that is left is doing the test, by solving it.