The center of a circle is A (-3,3), and B (1,6) is on the circle. Find the area of the circle in terms of pi.
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[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 3}})\quad % (c,d) &({{ 1}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{[1-(-3)]^2+[6-3]^2}\implies r=\sqrt{(1+3)^2+(6-3)^2} \\\\\\ r=\sqrt{4^2+3^2}\implies r=\sqrt{25}\implies \boxed{r=5}\\\\ -------------------------------\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad r=5\implies \boxed{A=25\pi }[/tex]
Related Questions
The isometric dot paper shoes 2 vertices 1 edge of the cube structure . Complete the isometric drawing
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Given the sequence: {2, 8, 32, 128, 512…}, S12 = ???
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8/2 = 4
32/8 = 4
128/32 = 4
512/128 = 4
The common ratio is 4. The equation for geometric sequence for the sum of terms is:
[tex]S_{n} = \frac{ A_{1}( r^{n}-1) }{r-1} [/tex]
where n is the last term of the progression
A1 is the first term of the progression
r is the common ratio
Substituting the values,
[tex]S_{12} = \frac{2( 4^{12}-1) }{4-1} [/tex]
S12 = 11,184,810
Select all that apply. Which of the following ratios are equivalent?
A. 3 to 4
B. 3/4
C. 6/7
D. 15/20
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Answer:
A,B,D
Step-by-step explanation:
Find the area of an equilateral triangle with radius 22 cm. Round to the nearest whole number.
629 cm2
363 cm2
982 cm2
1257 cm2
Answers
This measurement of the radius is the hypotenuse of the 30°-60°-90° triangle formed with the half the measurement of the side of the equilateral triangle being opposite to the 60° and equal to the hypotenuse times (1/2)(√3)
If we let s be the side of the triangle then,
s/2 = r(1/2)(√3)
Multiplying the equation by 2,
s = r√3
Substituting,
s = (22 cm)(√3) = 22√3
The area of the equilateral triangle is computed through the equation,
A = (√3 / 4)(s²)
Substituting,
A = (√3 / 4)(22√3)² = 628.7 cm²
Therefore, the answer to this item is the first choice.
The howler monkeys at a zoo are fed a diet that contains 3.35 kcal/gram. Write a function g(x) that gives the mass of food in grams that a howler monkey must eat to obtain x kilocalories of energy.
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For this item, we assume that g(x) is the total energy that the howler monkey needs to obtain and x is the amount of food in grams. From the presented concept in the first paragraph,
amount of energy = (3.35 kcal/gram) x (amount of food)
g(x) = 3.35x
Find the value of x in the figure below. Round to the nearest tenth.
6.7
20
4
15
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on a particular day, the Dow Jones had a rate of change of 2.8%. Which of the following statements must also be true?
-The average of the 30 stocks in the Dow Jones increased.
-The NASDAQ decreased.
-The S&P 500 increased.
-Every stock in the Dow Jones increased.
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Answer
THE AVERAGE OF THE 30 STOCKS IN THE DOW JONES INCREASED
Step-by-step explanation:
How would you write 0.00568 in scientific notation?
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Four graphs are shown below:
Which graph best shows the line of best fit?
Graph A
Graph B
Graph C
Graph D
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Find the volume of this oblique pyramid.
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nutrient level required to maintain energy and growth what is it called
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%) points. Brainliest.
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
C = 5/9 (F − 32)
Which of the following formulas correctly solves for F?
F = 9/5C + 32
F = 9/5C − 32
F = 9C + 32/5
F = 9C − 32/5
Hugh has to earn at least $400 to meet his fundraising goal. He has only 100 books that he plans to sell at $8 each. Which inequality shows the number of books, x, Hugh can sell to meet his goal?
20 ≤ x ≤ 400
40 ≤ x ≤ 100
50 ≤ x ≤ 400
50 ≤ x ≤ 100
Mike observed that 75% of the students of a school liked skating. If 35 students of the school did not like skating, the number of students who liked skating was ______. (only put numeric values, no other symbols)
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Let's take the first question, we have to turn the equation [tex]C = 5/9 (F − 32)[/tex] into a formula that correctly solves for F. First, let's switch the sides of the equation.
[tex]\frac{5}{9}\left(F-32\right)=C[/tex]
Divide both sides by 5/9. We are doing this to undo the multiplication.
[tex]\frac{\frac{5}{9}\left(F-32\right)}{\frac{5}{9}}=\frac{C}{\frac{5}{9}}[/tex]
[tex]F-32=\frac{9C}{5}[/tex]
Add 32 to both sides.
[tex]F-32+32=\frac{9C}{5}+32[/tex]
[tex]F=\frac{9C}{5}+32[/tex]
We have successfully gotten the formula to get F.
For the second question, we could use a graph for this. Since we want to reach the 400, then the inequality should reach that too. We should be careful though, since the profit will depend on the number of books you will sell, then the profit should be on the y-axis, and the number of books should be on the x-axis. The answer would be 50 ≤ x ≤ 100
For the third question, we can also infer that the 35 students that did not like skating should represent the 25% of the students. So, we could set up a proportion.
[tex] \frac{35}{25} = \frac{x}{75} [/tex]
We would then multiply, and then divide.
[tex](35*75)/25=105[/tex]
Now we know that the number of students who liked skating was 105 students.
-TetraFish
9c + 32/5=f this is the answer
i think
A quadrilateral has three angles that measure 90o , 100o, and 120o. which is the measure of the fourth angle?
Answers
the measure of the fourth angle = 360 - 90 - 100 - 120 = 50°
Answer: The measure of the fourth angle of the given quadrilateral is 50°.
Step-by-step explanation: Given that a quadrilateral has three angles that measure 90° , 100° and 120°.
We are to find the measure of the fourth angle of the quadrilateral.
Let x° be the measure of the fourth angle of the quadrilateral.
We know that
The sum of the measures of the four angles of a quadrilateral is 360°.
So, for the given quadrilateral, we have
[tex]90^\circ+100^\circ+120^\circ+x^\circ=360^\circ\\\\\Rightarrow 310^\circ+x^\circ=360^\circ\\\\\Rightarrow x^\circ=360^\circ-310^\circ\\\\\Rightarrow x^\circ=50^\circ.[/tex]
Thus, the measure of the fourth angle of the given quadrilateral is 50°.
Someone help me fast please
Answers
6 * (4+2)^2 -3^2 =
6 * 6^2 -3^2 =
6* 36-9 =
216-9=
207
Answer is C. 207
A rectangle with vertices located at (1, 2), (1, 5), (3, 5), and (3, 2) is stretched horizontally by a factor of 3 with respect to the y-axis. What is the area of the image that is produced?
Answers
Now the y is stretched 3 times, so the area will increase 3 times too, which is 18
Write an expression for m∠ RST
3x – 9
6x – 18
1.5x – 4.5
6x – 9
This is duplicate version of the question i forgot to add a picture to it
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so mRST = 2 (3x - 9)
= 6x - 18
Final answer:
The expressions provided are different forms of similar linear expressions, which could potentially describe the measure of angle RST if related algebraically or geometrically. The expression for m∠ RST is 6x - 9
Explanation:
Calculating the measure of angle RST involves understanding that the angles around a point add up to 360°, and the angles on a straight line add up to 180°. Based on the provided expressions, we are likely looking for the expression that adheres to these geometric rules.
The expressions given are: 3x – 9, 6x – 18, 1.5x – 4.5, and 6x – 9. To determine which one correctly represents the measure of angle RST, we would need some context from the problem or a diagram. However, assuming a relationship between the expressions and angle RST using linear or angular sums, we can observe that the expressions 3x – 9 and 6x – 18 are equivalent (by factoring out a 2 from the second expression), and similarly, 1.5x – 4.5 is equivalent to 3x – 9 upon multiplying by 2. The expression 6x – 9 could also be related if RST formed a linear pair with another given angle.
Solve for x: (3x−2)(2x+3)=0
Answers
(3x−2)=0; x = 2/3
(2x+3)=0; x = -3/2
answer
x = -3/2 and x = 2/3
(3x -2)(2x +3) = 0
6x² + 5x - 6 = 0
Now we have to factor the left side
(3x -2)(2x +3) = 0
Set factors equal to 0
3x -2 =0 or 2x + 3 =0
3x = 0 + 2 or 2x= 0 -3
3x = 2 or 2x = -3
x = 2/3 or x =-3/2
I hope that helps!
what is the value of m in the equation 4m + 2(m + 1) = 9m + 5
Answers
4m+2(m+1)=9m +5
4m+2m+2=9m+5
6m+2=9m+5
6m+2-6m= 9m+5-6m
2-5=3m+5-5
-3/3=3m/3
m=-1
A 20 sided die is rolled. What is the probability that a 1 is rolled?
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The graphs of functions f(x) and g(x) = f(x) + k are shown below:
graph of line f of x going through ordered pairs 0, 0 and 2, 4. Graph of line g of x going through ordered pairs 0, 2 and 1.5, 5.
The value of k is ___.
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[tex] m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]
gives us a slope equation of:
[tex]m= \frac{4-0}{2-0} [/tex] and the slope is 2. Using the point (0, 0) to write the equation of the line for f(x) looks like this in the slope-intercept form of the equation:
[tex]y- y_{1} =m(x- x_{1}) [/tex] where m is the sloppe of 2 that we found and [tex] y_{1} [/tex] and [tex] x_{1} [/tex] are the coordinates of one of the points. It doesn't matter which one you choose; you will get the same answer whether you use (0, 0) or (2, 4): y-0=2(x-0) Distributing that 2 into the parenthesis and simplifying gives you the equation of y = 2x, or in our function notation, f(x) = 2x. Since f(x) is the first part of g(x), so far for g(x) we have that g(x) = 2x + k. Now we will do the same thing for g(x) that we did for f(x) as far as writing its equation down; we don't need to find the slope cuz the slope of g(x) is the function f(x). The equation for g(x), using the point (0, 2) (again, you could have used either point; I just picked (0, 2) cuz the other one has a decimal in it!): y - 2 = 2(x - 0). Distributing that 2 into the parenthesis gives you this: y - 2 = 2x - 0; y = 2x + 2. So 2 is your k value!
A kite with a string 50 meters long makes an angle of elevation of 58o with the ground, assuming the string is straight, how high is the kite? Round your answer to the nearest tenth of a foot.
Answers
An angle of elevation of 58 degrees with the ground means that the angle started at the x-axis and terminates on the first quadrant region through a counter clockwise direction. Imagining a triangle, the string of the kite becomes the hypotenuse, the angle 58 degrees is the angle between the hypotenuse and the ground, and the height of the kite is the side opposite to the angle.
Therefore, we can calculate for the height of the kite using the sin function:
sin θ = opposite side / hypotenuse
sin 58 = opposite side / 50 m
opposite side = 50 m * sin 58
opposite side = 42.4 m
Therefore the kite is about 42.4 m above the ground.
Solve for x: 5 over quantity x squared minus 4 plus 2 over x equals 2 over quantity x minus 2
Answers
5/((x-2)(x+2))+2/x=2/(x-2), to add/subtract fractions we need a common denominator, so in this case we need a common denominator of x(x-2)(x+2) so
5(x)+2(x+2)(x-2)=2(x)(x+2), perform indicated operations...
5x+2(x^2-4)=2x(x+2)
5x+2x^2-8=2x^2+4x subtract 2x from both sides
5x-8=4x subtract 4x from both sides
x-8=0 add 8 to both sides
x=8
check...
5/(x^2-4)+2/x=2/(x-2) when x=8 so
5/(64-4)+2/8=2/(8-2)
5/60+1/4=2/6
5/60+15/60=20/60
20/60=20/60
a man divided $9000 among his wife , son and daughter. the wife received twice as much as the daughter and the son received $1000 more than the daughter how much did each receive
with working please
thank you
Answers
2D. D+1000. D
9000= 2d + D+1000 + D
9000= 4d + 1000
-1000
8000=4d
D=2000
So the daughter got 2000$
The son got 3000$ because it's 1000 more than the daughter which is 2000
And the mom got 4000 which is twice the daughters.
You can check by adding them together. 2000+3000+4000 is 9000.
Indicate the method you would use to prove the two 's . If no method applies, enter "none".
SSS
SAS
ASA
AAS
None
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The simpliest way is to use the AAS Postulate.
AAS Postulate: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
From the diagram you have:
1. one pair of angles with measure 40°;
2. one pair of angles with measure 60°;
3. the non-included side of one triangle is congruent to the non-included side of another triangle (their lengths are 10).
Answer: correct choice is D (AAS)
Answer:
AAS postulate :)
Step-by-step explanation:
c. When the center of Earth is 2 × 1011 meters from the center of Mars, the force of gravity between the two planets is about 64.32 × 1014 newtons. The mass of Earth is about 6 × 1024 kilograms, and the mass of Mars is about 6.4 × 1023 kilograms. Using these values, estimate the gravitational constant.
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To estimate the gravitational constant (G), we apply Newton's law of universal gravitation, using the provided values of the force of gravity between Earth and Mars, the masses of both planets and their distance apart. The calculation yields an estimated G value of approximately 6.67 × 10⁻¹¹ N·m²/kg², which aligns with the known gravitational constant.
Explanation:To estimate the gravitational constant (G), we can use Newton's law of universal gravitation, which states that the force of gravity (F) between two masses (m₁ and m₂) is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers:
F = G * (m₁*m₂) / r²
Given that:
The force of gravity (F) between Earth and Mars is approximately 64.32 × 10¹⁴ newtons.The mass of Earth (m₁) is about 6 × 10²⁴ kilograms.The mass of Mars (m₂) is about 6.4 × 10²³ kilograms.The distance between the centers of Earth and Mars (r) is 2 × 10¹¹ meters.We can rearrange the formula to solve for G:
G = F * r² / (m₁ * m₂)
Plugging in the values:
G = (64.32 × 10¹⁴ N) * (2 × 1011 m)² / (6 × 10²⁴ kg * 6.4 × 10²³ kg)
G ≈ 6.67 × 10⁻¹¹ N·m²/kg²
This value is approximately equal to the known gravitational constant, solidifying our understanding of gravitational forces and confirming the validity of our calculations.
if the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? a. 3,900.00 b. 3,947.00 c. 3,977.40 d. 4,000.00
Answers
A=p (1+r)^t
A future value 4370.91
P present value?
R interest rate 0.03
T 3years
We need to solve for p
P=A÷(1+r)^t
P=4,370.91÷(1+0.03)^(3)
P=4,000.00
Factor the GCF from 96x2 + 88x. Use the drop-down menus to complete the statements. The GCF of 96x2 and 88x is . Each term written as a product, where one factor is the GCF, is . The factored form of the expression is
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=> Decompose each number in their prime numbers:
=> 96 = (2^5)(3)
=> 88 = (2^3) (11)
=> GCF of 96 and 88 = 2^3 = 8
2) Determine the GCF of the letters, x^2 and x
=> x
3) Conclude the GCF of the terms is 8x
4) Now you can factor the expression by dividing each term by the GCF, 8x:
96 x^2 / (8x) = 12x
88x / (8x) = 11
So, the factored form is (8x) (12x + 11)
Answer:
1: The GCF of 96x2 and 88x is: Answer: 8x
2: Each term written as a product, where one factor is the GCF, is: Answer: 8x(12x)+8x(11)
3: The factored form of the expression is: Answer: 8x(12x+11)
Step-by-step explanation:
You're explanation is the answers hope I helped !!!! Good luck!!!!!
Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0
Answers
The solution of the given quadratic equation will be ( -5, 0 ).
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
Given equation is:-
x² = -5x
x² + 5x = 0
x ( x + 5 ) = 0
x = 0 and x = -5
Therefore the solution of the given quadratic equation will be ( -5, 0 ).
To know more about quadratic equations follow
https://brainly.com/question/1214333
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The solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex] can be calculated after modifying the quadratic equation and rewriting it to [tex]x^{2} + 5x + 3 = 0[/tex], and then this can be calculated using the quadratic formula. The solutions are x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex]and x =[tex]\frac{{-5 - \sqrt{13}}}{2}[/tex] .
To find the solutions to the quadratic equation [tex]\(x^2 = -5x - 3\)[/tex], let's first rewrite it in the standard form:
[tex]\[x^2 + 5x + 3 = 0\][/tex]
Now, we can use the quadratic formula to find the solutions:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Where a = 1,,b = 5, and c=3.
[tex]\[x = \frac{{-5 \pm \sqrt{{5^2 - 4 \cdot 1 \cdot 3}}}}{{2 \cdot 1}}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{{25 - 12}}}}{2}\][/tex]
[tex]\[x = \frac{{-5 \pm \sqrt{13}}}{2}\][/tex]
So, the solutions are:
x =[tex]\frac{{-5 + \sqrt{13}}}{2}[/tex] and [x = [tex]\frac{{-5 - \sqrt{13}}}{2}[/tex]
In the game of blackjack, determine the odds of dealing yourself a blackjack (ace plus face-card or 10) from a single deck. show how you arrived at your answer.
Answers
There are 52 possibilities for the first card, 51 for the second for 2652 total possible first/second card combinations so the odds of dealing a blackjack are 128/2652, which reduces to 32/663 odds
Final answer:
The odds of dealing yourself a blackjack in a single deck game of blackjack, by drawing an ace and a face card or 10 in either order, is 128 out of 2652, which simplifies to approximately 1 in 20.7.
Explanation:
In the game of blackjack, to determine the odds of dealing yourself a blackjack (ace plus a face card or 10), we need to calculate the probability of drawing an ace and then a ten-value card, or vice versa, from a single deck. A standard deck of cards has 52 cards, with 4 aces and 16 ten-valued cards (10, J, Q, K across four suits). The probability of drawing an ace first is 4 out of 52, and then a ten-value card is 16 out of 51. Alternatively, the probability of drawing a ten-value card first is 16 out of 52, and then an ace is 4 out of 51.
The total probability is the sum of both probabilities:
Probability of Ace first, then ten-value card: (4/52) * (16/51)Probability of ten-value card first, then Ace: (16/52) * (4/51)We then add these two probabilities together to find the total probability of dealing a blackjack from a single deck.
The total probability is (4/52) * (16/51) + (16/52) * (4/51) which simplifies to (64/2652) + (64/2652), or 2 * (64/2652), which simplifies further to (128/2652). Therefore, the odds of dealing a blackjack are 128 out of 2652, or approximately 1 in 20.7 when simplified.
,[PICTURE INCLUDED] Kite CDEF is rotated 180° about the origin and translated 3 units up to form kite WXYZ. If CD is x units long, what is the length of WX?
Answers
he 2 kites are identical
CD is the same as WX
so it would be x +0
answer is A