Final answer:
To find the equation of the circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). Using the distance formula, the radius is found to be 5. Therefore, the equation of the circle is [tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex].
Explanation:
To find the equation of a circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). We can use the distance formula to find the radius, which is the distance between the center and the point on the circle.
Using the distance formula, [tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex], we have:
[tex]d = \sqrt{((0 - 3)^2 + (2 - (-2))^2)} = \sqrt{((-3)^2 + (4)^2)} = \sqrt{(9 + 16)} = \sqrt{(25)} = 5[/tex]
So, the radius is 5. Therefore, the equation of the circle is
[tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex]
To find the equation of the circle with center at (3, -2) and passing through the point (0, 2), use the standard form and calculate the radius. Then, the equation is (x - 3)² + (y + 2)² = 25.
To find the equation of a circle with center at (3, -2) and passing through the point (0, 2), we can use the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle, and r is the radius. Given the center (3, -2), we substitute h = 3 and k = -2:
(x - 3)² + (y + 2)² = r².
Next, we find the radius by calculating the distance between the center (3, -2) and the point (0, 2) using the distance formula:
r = [tex]\sqrt{(0 - 3)^2 + (2 + 2)^2}[/tex]
= √(9 + 16)
= √(25)
= 5.
With r = 5, we can now write the full equation of the circle:
(x - 3)² + (y + 2)² = 25
To summarize, the equation of the circle with center at (3, -2) and passing through the point (0, 2) is (x - 3)² + (y + 2)² = 25.
Plz help.. btw this is 7th grade math. (22 pts.)
A killer whale has eaten 75 pounds of fish today. It needs to eat at least 140 pounds of fish each day. a. A bucket holds 15 pounds of fish. Identify an inequality that represents how many more buckets x of fish the whale needs to eat.
Answer:
He needs 4 1/3 buckets of fish.
Step-by-step explanation:
140 - 75 = 65 pounds of fish left to eat
15x = 65
x = 65 / 15
x = 4 1/3 buckets of fish left to eat
Help plzzzzz ASAP I NEED HELP
Answer:
a
Step-by-step explanation:
all that happned was community property if numbers are switced around in an addition sentence then the answer will always be the same
the formula for blood flow rate can be described by the formula f=N-O/R are where F represents the blood flow rate, N represents the pressure in the inlet, O represents the pressure in the outlet, and R representative vascular resistance
True or false: The following equation is correctly solved for the vascular resistance.
R=F+O-N
Answer:
FALSE
Step-by-step explanation:
F = (N - O)/R Multiply both sides by R
RF = N – O Divide both sides by F
R = (N – O)/F
FALSE. The given solution is incorrect.
Final answer:
The statement provided is false. The correct formula for vascular resistance R in terms of blood flow F, inlet pressure N, and outlet pressure O should be R = (N - O) / F.
Explanation:
The statement is false. The correctly solved equation for vascular resistance R, based on the formula F = (N - O) / R where F is blood flow rate, N is the pressure at the inlet, O is the pressure at the outlet, would be R = (N - O) / F. If we isolate R in the equation by multiplying both sides by R and dividing by F, we would get R = (N - O) / F, not R = F + O - N as incorrectly stated in the question.
To further understand the relationships among the factors affecting blood flow, the Poiseuille's equation plays a significant role. This equation includes critical variables like the radius (r) to the fourth power, vessel length (λ), and viscosity (n) of the fluid. Changes in these variables can significantly affect blood flow and resistance within the vascular system.
find the value of x
Answer:
x = 0.1
hope this is helpful
During a race, a runner’s time was 4 seconds at the 36-meter mark and 6 seconds at the 57-meter mark. What was the runner’s average speed, in meters per second, for the time interval between 4 seconds and 6 seconds? (A) 2.1 (B) 9.0 (C ) 9.3 (D)9.5 (E) 10.5
i need help ASAP ):
Answer:
E
Step-by-step explanation:
57 - 36 = 21 6 - 4 = 2 seconds
21 ÷ 2 = 10.5
Answer:
The average speed of runner is given by option d) 10.5 meters per second.
Step-by-step explanation:
We are given the following information in the question:
A runner’s time was 4 seconds at the 36-meter mark.
A runner’s time was 6 seconds at the 57-meter mark.
Formula:
[tex]\text{Average speed} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\\text{where}, y_2, y_1 \text{are the distances at time} x_2, x_1 \text{respectively.}[/tex]
Putting the given values in the question, we have:
[tex]\text{Average speed} = \displaystyle\frac{57-36}{6-4} = \frac{21}{2} = 10.5\text{ meter per second}[/tex]
Hence, the average speed of runner is given by option d) 10.5 meters per second.
If f(x)=6x^2-3 and f(x)=3 then what is the value of x
[tex]f(x)=6x^2-3,\ f(x)=3\\\\\text{The equation}\\\\6x^2-3=3\qquad\text{add 3 to both sides}\\\\6x^2=6\qquad\text{divide both sides by 6}\\\\x^2=1\to x=\pm\sqrt1\\\\\boxed{x=-1\ \vee\ x=1}[/tex]
a cookie costs .45 and a cupcake costs .65. thirty five baked goods were sold for a total of 18.55. how many cookies were sold?
Answer:
14 cookies were baked
Step-by-step explanation:
Using a system of equations, we find that 21 cookies were sold after setting up the equations based on cost per item and total sales, and solving for the two variables representing cookies and cupcakes.
The student's question is about how many cookies were sold given that a cookie costs $0.45 and a cupcake costs $0.65, and 35 baked goods in total were sold for $18.55.
To solve this, we can set up a system of equations:
Let x represent the number of cookies sold.
Let y represent the number of cupcakes sold.
We are given two equations based on the problem statement:
x + y = 35 (since 35 total baked goods were sold)
0.45x + 0.65y = 18.55 (since the total cost of the goods sold was $18.55)
Solving the system of equations, we first multiply the first equation by 0.45:
(1) 0.45x + 0.45y = 15.75
Subtract this from the second equation:
0.20y = 2.80 (subtracting the first modified equation from the second original equation)
Divide both sides by 0.20 to find y:
y = 14
Then we substitute y into the first equation to find x:
x + 14 = 35
x = 21
So 21 cookies were sold.
What is 11/16 as a percent
⭕ 11\16= %
⭕ 11÷16= 68.75%
⭕ 68.75%
To convert a fraction to a percentage, we would multiply the fraction by 100%, and the result would be the percentage.
In this case:
11/16 x 100%
=0.6875 x 100%
=68.75%
Therefore the answer is 68.75%
Hope it helps!
In 1992, Jason bought a gallon of gas for $1.23. Yesterday, he bought a gallon of gas for $2.09. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent. A. 30.1% B. 41.1% C. 58.9% D. 69.9%
Answer:
47.8% increase, or B since it's the closest.
Step-by-step explanation:
Answer:The answer to this problem is actually 69.9%
Step-by-step explanation:
Please answer this correctly
Answer:
$22.1
Step-by-step explanation:
To solve this, you must multiply the amount of the items by its cost.
This is the amount of yams in decimal form: [tex]4\frac{1}{2}[/tex] = 4.5
This is the amount of carrots in decimal form: [tex]4\frac{3}{10}[/tex] = 4.3
4.5 * 3 = 13.5
4.3 * 2 = 8.6
Now we add them together to get the total cost.
13.5 + 8.6 = 22.1
Answer:
$22.10
Step-by-step explanation:
This is simple multiplication.
1. It may help you to simplify the pound values. 4 and 1/2 is really 4.5, and 4 and 3/10 is really 4.3
2. We know what the cost is per pound, and we know how many pounds we have. We simply multiply.
4.5 pounds of yams * $3 per pound = 13.5
4.3 pounds of carrots * $2 per pound = 4.3*2 = 8.6
3. Add the values
13.5+8.6 = 22.1 = $22.10
How do I graph this?
Answer:
Step-by-step explanation:
you're going to have a vertical line at -1, and then shade the region to the left. The line should be dashed, not solid.
Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of 0.04 liters. Then, he wants to fill the tank with water until it's completely full. If he uses 50 marbles, he will have to add 33 liters of water. What is the volume of the tank?
Answer: 35 liters
Step-by-step explanation:
Volume of 1 marble = 0.04 Liters
volume of 50 marbles = 50 x 0.04 liters = 2 liters
volume of water added = 33 liters ( Given)
Volume of tank = Volume of water + Volume of 50 marbles
= 33 liters + 2 liters
= 35 liters
The distance coordinates D(-4,-3)and E(5,9)
Answer:
the answer is is 225
Step-by-step explanation
(5 - - 9)^2 + (8 - -3)^2
(9)^2 + (12)^2
81 +144
225
Answer:
The answer is 6.1
Step-by-step explanation:
(-4,3)(5,9)
√(-4-5)^2 + (3 - 9)^2
√-1^2 + -6^2
√1 + 36
√37
= 6.1
If f(x)=3x-15, what is f(4)?
Answer:
x=6.33
Step-by-step explanation:
4=3x-15
19=3x
6.33=x
f(4) This means that x is 4, so you can plug in 4 for "x" in the equation
f(x) = 3x - 15
f(4) = 3(4) - 15
f(4) = 12 - 15
f(4) = -3
Drag each tile to the correct box. Arrange the complex numbers in order according to the quadrant in which they appear, starting with the first quadrant. (3 − 4i) (-1 − 3i) (4 + i) (-2 + 2i)
Answer:
see explanation
Step-by-step explanation:
(4 + i) → first quadrant
(- 2 + 2i) → second quadrant
(- 1 - 3i) → third quadrant
(3 - 4i) → fourth quadrant
why is 4b-7-3b+9 equal to b+2
What is the measure of 1 in the trapezoid?
110°
55°
165°
85°
Answer: The correct option is (B) 55°.
Step-by-step explanation: We are given to find the measure of angle 1 in the trapezoid shown in the figure.
We know that
one pair of sides of a trapezoid are parallel to each other.
As shown in the figure, the base of the trapezoid and its opposite side are parallel to each other.
Also, they are cut by a tranversal such that the angle 1 and the angle with measure 125° are interior angles on the same side of the transversal.
So, the sum of the measures must be equal to 180°.
That is,
[tex]125^\circ+m\angle 1=180^\circ\\\\\Rightarrow m\angle 1=180^\circ-125^\circ\\\\\Rightarrow m\angle 1=55^\circ.[/tex]
Thus, the required measure of angle 1 is 55°.
Option (B) is CORRECT.
at a clothing store 3 shirts and 8 hats cost $65. the cost for 2 shirts and 2 hats is $30. how much does each shirt and hat cost
Answer:
For the $30 2 shirts and 2 hats each one would be $7.50.
For the $65 3 shirts and 8 hats each one would be $5.90
Step-by-step explanation:
Answer:
A shirt x cost $11
and a hat y cost $4
Step-by-step explanation:
Step one
This is a word problem and we can tackle it by expressing it Mathematically
Let us initialize shirt as "x" and hat as "y"
Now
1. 3 shirts and 8 hats cost $65
Mathematically
3x+8y= 65 - - - - - - - 1
2. the cost for 2 shirts and 2 hats is
$30
Mathematically
2x + 2y = 30---------2
We now have two equations with two unknowns
We can solve for the unknown simultaneously
Step a. Multiply equation one by 1
And equation two by 4
3x+8y= 65 - - - - - - - 1
8x + 8y = 120------------2
Step b
Subtracting equation one from two
3x+8y= 65 - - - - - - - 1
-(8x + 8y = 120) ------------2
=-5x+0=-55
-5x=-55
5x=55
x=55/5
x=11
Substituting the value of x in any of the equation above to solve for y say equation 2
2(11) + 2y = 30
22+2y=30
2y= 30-22
2y= 8
y= 8/2
y= 4
Hence a shirt x cost $11
And the hat y cost $4
PLZ HURRY
Which graph represents the function f(x) = 2|x|?
Answer:
the third one............ not the second
Step-by-step explanation:
The graph of the absolute function f(x) = |2x| is option B
What is graph of an absolute function?The graph of an absolute function, also known as an absolute value function, is a V-shaped graph that is symmetric with respect to the y-axis. The absolute value function is defined as:
f(x) = |x|,
where |x| represents the absolute value of x.
The graph of the absolute value function consists of two parts:
For x ≥ 0, the function f(x) = x. This portion of the graph appears as a straight line with a positive slope, starting from the origin (0,0) and extending upwards to the right.For x < 0, the function f(x) = -x. This portion of the graph is also a straight line with a positive slope, starting from the origin (0,0) and extending upwards to the left.Using a graphing calculator;
f(x) = 2|x|
The graph of the function is attached below;
From the graph attached below the answer is option B.
Learn more on graph of an absolute function here;
https://brainly.com/question/25910324
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in decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?
0.2
0.3
0.4
0.5
Answer: 0.4 which is choice C
====================================
Work Shown
Focus on the "riverside high school" row only
A = number of twelfth graders = 200
B = number of students = 500
P = probability of picking a twelfth grader
P = A/B
P = 200/500
P = 2/5
P = 0.4
The probability that a randomly selected riverside high school student is in twelfth grade is 0.4
What is probability?The probability of an event occurring, it is calculated by the ratio of favorable cases to the total number of possible cases.
P(Event) = Favorable outcomes/ Total no. of outcomes
Now, the total no. of students studying in Riverside High School = 500
The no. of students studying in 12th grade in Riverside High School= 200
P(student in 12th grade in Riverside High School) = 200/500
P(student in 12th grade in Riverside High School) = 0.4
Hence the probability that a randomly selected riverside high school student is in twelfth grade is 0.4.
Learn more about probability on:
https://brainly.com/question/24756209
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Find the smallest rectangular area of wrapping paper that can be used to wrap a preant that is 22 inches by 20 inches by 10 inches. The paper cannot be cut
Answer:
do it urself
Step-by-step explanation:
The surface area of a box is the sum of the areas of all the rectangular faces of the box.
Let length = x
Let width = y
Let height = h
SA = 2xy + 2xh + 2yh
Plug in the given values into the formula to find the area.
SA = 2(32)(25) + 2(32)(20) + 2(25)(20)
PLEASE HELP 49 POINTS@
show your work!
Answer:
Step-by-step explanation:
Yes it is because it can be written in the form y=kx.(y=5/9x)
The constant variation would be 5/9.
Pretty sure this is correct but if not, sorry! Hope this helps.
Answer:
This is a direct variation where the constant of variation is 5/9
Step-by-step explanation:
The equation for direct variation is y = kx
5x-9y =0
Lets try to get this equation in the above form
Add 9y to each side
5x-9y +9y = 9y
5x = 9y
Divide each side by 9
5/9 x = 9y/9
5/9x = y
This is in the form y = k x where k =5/9
Eli's office recycled a total of 12 kilograms of paper over 6 weeks. After 9 weeks, how many kilograms of paper will Eli's office have recycled
[tex]\begin{array}{ccc}6\ weeks&-&12\ kg\\9\ weeks&-&x\ kg\end{array}\qquad\text{cross multiply}\\\\(6)(x)=(9)(12)\\\\6x=108\qquad\text{divide both sides by 6}\\\\\boxed{x=18}\\\\Answer:\ \text{Eli's office recycled 18\ kg\ of\ paper.}[/tex]
The weights (in pounds) of 18 preschool children are
32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29
Answer:
22.8 and 37.5
Step-by-step explanation:
Given the
The weights (in pounds) of 18 preschool children are
32, 20, 25, 27, 31, 22, 30, 23, 44, 37, 33, 45, 41, 24, 34, 21, 39, 29
To find its 20th percentile and 75th percentile.
In ascending order we get like this
Position X (Asc. Order)
1 20
2 21
3 22
4 23
5 24
6 25
7 27
8 29
9 30
10 31
11 32
12 33
13 34
14 37
15 39
16 41
17 44
18 45
Percentile position = (no of entries +1)20/100 = 19/5 = 3.8
Since posiiton is not integer we use interpolation method.
The value of 3.8 - 3 = 0.8 corresponds to the proportion of the distance between 22 and 23 where the percentile we are looking for is located at.
Hence 20th percentile = [tex]22+0.8(23-22)=22.8[/tex]
So answer is 22.8
----------------------
75th percentile
Percentile posiiton = 19(75)/100 = 14.25
75th percentile= [tex]37+0.25(39-37)=37.5[/tex]
Answer:
22.8 and 37.5
Solve the quadratic equation: 2x2 + 11x − 6 = 0
Answer:
see explanation
Step-by-step explanation:
To factorise the quadratic consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term.
product = 2 × - 6 = - 12 and sum = + 11
The factors are + 12 and - 1
Use these factors to split the middle term
2x² + 12x - x - 6 = 0 ( factor the first/second and third/fourth terms )
2x(x + 6) - 1(x + 6) = 0 (factor out (x + 6) )
(x + 6)(2x - 1) = 0
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
2x - 1 = 0 ⇒ x = [tex]\frac{1}{2}[/tex]
can someone help with this
Answer: Draw a line through the two points (0,2) and (3,3). See the attached image below.
How did I get these two points? The first point comes from the fact that "at the start, the height is 2 inches" meaning that x = 0 hours and y = 2 inches pair up together. This is show as point A. This is the y intercept as this is the location where the blue graph crosses the vertical y axis.
Point B is found by moving 1 unit up from point A and 3 units to the right to land on (3,3). So we have x = 3 hours and y = 3 inches pair up together.
Note: the slope is rise/run = 1/3 helping us determine the unit rate or speed in which the water is rising (ie the water is rising one-third of an inch per hour)
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 249,583. Its current population is 318,270. By about what percentage has the city grown over the past ten years?
Answer:
27.52 percent
Step-by-step explanation:
Percentage increase = (new - original)/ original * 100
new = 318270
old = 249583
Substitute in what we know
percentage increase = (318270-249583)/249583 *100
= (68687/249583) *100
.275207045*100
27.5207045 percent
Answer:
28%
Step-by-step explanation:
Please help need this answer
Answer:
There are no solutions
Step-by-step explanation:
4x-1 = 2(2x-1)
The first step is to distribute the 2
4x-1 = 2*2x-2*1
4x-1 = 4x-2
Subtract 4x from each side
4x-4x-1 = 4x-4x-2
-1=-2
Since this is not true, there are no solutions
Brainliest + Points!
Does anyone know how to do this?
For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution.
{55, 54, 66, 38, 53, 56, 57, 66, 45, 65}
A.
50%; This percentage is lower than expected in a normal distribution.
B.
60%; This percentage is lower than expected in a normal distribution.
C.
70%; This percentage is close to the expected percentage in a normal distribution.
D.
80%; This percentage is higher than expected in a normal distribution.
Answer:
A. 50%; This percentage is lower than expected in a normal distribution
Answer:
A) 50%; This percentage is lower than expected in a normal distribution.
Step-by-step explanation:
Data points given:
55, 54, 66, 38, 53, 56, 57, 66, 45, 65
n = 10
The mean for the data points:
[tex] \frac{55+54+66+38+53+56+57+66+45+65}{10} [/tex]
Mean = 55.5
Standard deviation of data points:
[tex] = \sqrt{\frac{55-55.5)^2+(54-55.5)^2+(66+55.5)^2+(38-55.5)^2+(53-55.5)^2+(56-55.5)^2+(57-55.5)^2+(66-55.5)^2+(45-55)^2+(65-55)^2}{10}} [/tex]
= 8.59
Now let's find the data points that lie between 64.09 i.e (55.5 + 8.59) and 46.91 i.e (55.5-8.59)
We can see that 5 data points lie between 64.09 and 46.91 which are { 55,54,53,56,57}
The correct option is A, which states that 50% percentage is lowee than expected.
There are 24 members of the senate on the finance committee, how many different 13 member subcommittees can be chosen to review the current energy legislation
Answer:
2496144
Step-by-step explanation:
Total number of members of the senate on the finance committee (n)= 24
Number of members in each subcommittee(r) = 13
We need to make use of the combinations formula
C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]
1) Plugging in the values of n and r into formula, we get
C(24,13) = [tex]\frac{24!}{13!(24-13)!}[/tex]
= [tex]\frac{24!}{13!*11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14*13!}{13!*11!}[/tex]
2) Cancelling out the 13! from the top and bottom, we get
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11!}[/tex]
= [tex]\frac{24*23*22*21*20*19*18*17*16*15*14}{11*10*9*8*7*6*5*4*3*2*1}[/tex]
3) Upon simplifying the numbers on the top and bottom, we get
C(24,13) = 2496144