Solution
For this case we have the following equation given by:
[tex](x-2)^2+(y-5)^2=49[/tex]The general equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And for this case by direct comparison we have:
[tex]r^2=49[/tex]Then we have:
[tex]r=\sqrt[]{49}=7[/tex]And the center si given by C=(h,k)
From the equation given we have:
[tex]C=(2,5)[/tex]Below is a sample space for a family with 3 children. BGG stands for the oldest child being a boy, the middle child a girl, and the youngest a girl. Use the sample space to answer the question: What is the probability (in simplest form) that the oldest child is a a girl? _____Sample Space BBB BBG BGB BGG GBB GBG GGB GGG
The probability that the oldest child is a girl is given by the quotient between two numbers:
- The number of combinations where a girl is the oldest child i.e. the number of elements in the sample space that start with a G.
- The total number of elements in the sample space.
The first number is 4 since we have 4 elements starting with G: GBB, GBG, GGB, GGG. The second number is 8. Therefore the probability that we are looking for is given by:
[tex]P=\frac{4}{8}=\frac{1}{2}[/tex]AnswerThen the answer is 1/2.
Find the volume of the composite solid. Round your answer to the nearest hundredth,5.1 m5.1 mThe volume is about cubic meters,
The figure shows a cube with a cone shape extracted from it.
Thus, to get the volume of the composite solid, we need to subtract the volume of the cone from the volume of the cube.
i.e. Volume of Solid = Volume of Cube - Volume of Cone
[tex]\begin{gathered} \text{Volume of cube=}l\times l\times l=l^3 \\ l=5.1m\text{ (according to the question)} \end{gathered}[/tex]Therefore the volume of the cube is:
[tex]\text{Volume of cube = 5.1}^3=132.651m^3[/tex]Now we need to get the volume of the cone:
The formula of the volume of a cone is:
[tex]\begin{gathered} \text{Volume of cone = }\frac{1}{3}\times\pi\times r^2\times h \\ \\ r=\text{radius of cone} \\ h=\text{height of cone} \end{gathered}[/tex]The radius of the cone is the same as half the length of one edge of the cube
While the height of the cone is the same as the height of the cube.
A sketch is shown below:
Thus, height (h) of cone = 5.1m
radius (r) of cone = 2.55m
[tex]\text{Volume of cone=}\frac{1}{3}\times\pi\times2.55^2\times5.1=34.728m^3[/tex]Thus, we can now find the volume of the composite solid as:
[tex]\begin{gathered} \text{Volume of Composite Solid=} \\ 132.651m^3-34.728m^3 \\ \\ \therefore\text{Volume of Composite Solid=}97.923m^3\approx97.92m^3\text{ (To nearest Hundredth)} \end{gathered}[/tex]The volume is: 97.92 cubic meters
David and Victoria are playing ths integer card game. David drew three cards, -6, 12, and -4. What is the sum of the cards in his hands? Model your answer on the number line below. PLEASE HELP. Brainliest, will give.
The sum of -6 ,12 and -4 is,
[tex]\begin{gathered} S=-6+12-4 \\ S=2 \end{gathered}[/tex]Express it on number line implies,
the Browns build at a restaurant is $60 how much money should mr. Brown leave as a tip if he plans to tip 50%
We need to calculated first the 50% of $60
60*0.5=30
then we calculated the final bill
original bill + tip = money leave by mr Brown
60+30=90
he leave $90
Melissa won a week-long cruise in a contest and is working out the details of the trip. She can choose from 4 destinations and 5 departure dates. Since each cruise lets passengers pick one of 5 different day trips, Melissa also needs to choose one of those. How many different cruises can Melissa plan?
To solve this problem, it is necessary to use the fundamental counting principle, which is the multiplication counting rule.
It says that if we have two events, a and b. The total number of possible outcomes will be a times b (a*b).
In this case, a are the destinations she can choose and b are the departure dates. To find how many cruises can she plan, multiply the number of options of a and b, this is 4*5:
[tex]4\cdot5=20[/tex]In this case, she can plan 20 different cruises.
a school day is 8 hours how many minutes are in a school day
In order to solve this exercise you need to remember the following:
[tex]1\text{ }hour=60\text{ }minutes[/tex]In this case, based on the information given in the exercise, a school day is 8 hours. Then, you need to make the conversion from hours to minutes.
You can set up the following:
[tex](8\text{ }hours)(\frac{60\text{ }minutes}{1\text{ }hour})[/tex]Therefore, evaluating you get:
[tex]=\frac{(60\text{ }minutes)(8\text{ }hours)}{1\text{ }hour}=480\text{ }minutes[/tex]Hence, the answer is:
[tex]480\text{ }minutes[/tex]When the price of petrol increases by 20%,
a motorist decreases his volume of petrol
consumption by 10%. Find the percentage
increase in his petrol bill.
Answer:
The percentage increase in his petrol bill is 16 2/3%
The percentage increase in his petrol bill would be equal to 16 2/3%
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that When the price of petrol increases by 20%, a motorist decreases his volume of petrol consumption by 10%.
Let the inital price be 100 and consumption be 100t.
Now increased price
= 120 % of 100
= 120
New consumption
= 100 x 100 / 120
= 83.33
Hence, percentage reduction in the consumption will be;
(100 - 83.33)/ 100 x 100
16 and 2/3 %
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Which system of equations is represented by the graph?A. y = x + 4 y = x + 4/ x + 2B. y = x - 4 y = x + 4/ x + 2C. y = x + 4 y = x - 4/ x + 2D. y = x - 4 y = x - 4/ x + 2
Step 1. We have two equations represented in the graph. One is the red line and the other is the blue graph.
The red line represents a linear equation,
and the blue segments represent a rational equation.
Step 2. For the linear equations, we have only two options given:
[tex]\begin{gathered} y=x+4 \\ y=x-4 \end{gathered}[/tex]Graphing both lines to pick which one is the line shown in the problem:
The green line is y=x+4,
and the purple line is y=x-4.
Compared with our graph, we have the one that crosses the y-axis at -4, Thus it is the equation y=x-4.
Step 3. For the rational equation, we are given two options to choose from:
[tex]\begin{gathered} y=\frac{x+4}{x+2} \\ or \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]We graph the two equations to check which one is correct:
In the graph, we show in green
[tex]y=\frac{x+4}{x+2}[/tex]and in purple, we have the equation
[tex]y=\frac{x-4}{x+2}[/tex]As you can see, the second one, (the purple one) is the one shown in the graph from this problem, thus, the second equation is:
[tex]y=\frac{x-4}{x+2}[/tex]Answer: D
[tex]\begin{gathered} y=x-4 \\ y=\frac{x-4}{x+2} \end{gathered}[/tex]Which of the following words best completes this sentence? "The real roots of a quadratic equation correspond to the of the graph of the related function."
This is an example of a quadratic function
The real roots are where it crosses the x axis
Where it crosses the x axis are also called the zeros of the function or the x intercepts. They can also be called the roots of the quadratic.
Without the choices, I am unsure of the words to fill in the blank.
What would be the new coordinates of the figure below if it is translated the figure 4 units horizontally and -2 units vertically?
Given the coordinates of recatangle ABCD:
A(-3, 1), B(2, 1), C(2, -2), D(-3, -2)
Let's find the new coordinates after the rectangle is translated 4 units horizontally and -2 units vertically.
Let's apply rules of translation.
A translation 4 units horizontally means a shift 4 units to the right.
It is written as: (x + 4)
A translation -2 units vertically means a shift 2 units downwards.
It is written as: (y - 2)
Thus, to find the new coordinates, add 4 to the x-coordinates and subtract 2 from the y-cooridnates.
We have the translation rule: (x + 4, y - 2)
We have:
A(-3, 1) ==> (-3 + 4, 1 - 2) ==> A'(1, -1)
B(2, 1) ==> (2 + 4, 1 - 2) ==> B'(6, -1)
C(2, -2) ==> (2 + 4, -2 - 2) ==> C'(6, -4)
D(-3, -2) ==> (-3 + 4, -2 - 2) ==> (1, -4)
Therefore, the new coordintes of the figure are:
A'(1, -1), B'(6, -1), C'(6, -4), D(1, -4)
ANSWER:
A'(1, -1), B'(6, -1), C'(6, -4), D'(1, -4)
Simplify (3.8 x 10^-2)(5.14 x 10^-10). Write the final answer in scientific notation.
Answer:
1.9532×10⁻¹¹
Step-by-step explanation:
You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.
ProductThe product is computed in the usual way, making use of the rules of exponents.
(3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)
= 19.532 × 10^(-2-10) = 19.532 × 10^-12
Moving a factor of 10 from the coefficient to the exponent gives ...
= 1.9532×10^-11 . . . . . . final answer in scientific notation
__
Additional comment
Scientific notation has 1 digit to the left of the decimal point in the coefficient.
Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.
Your calculator can display the product in scientific notation for you, as can any spreadsheet.
Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.
<95141404393>
list the following information about the function: y = 2 (x-3)^2-1 (parent graph y = x^2)
Given
The function is defined as:
[tex]y\text{ = 2\lparen x -3\rparen}^2\text{ - 1}[/tex]x-intercepts
The x-intercepts of the function y are the values of x when y = 0
Substituting 0 for y and solving for x
[tex]\begin{gathered} 2(x-3)^2\text{ -1 = 0} \\ 2(x-3)^2\text{ = 1} \\ Divide\text{ both sides by 2} \\ (x-3)^2\text{ = }\frac{1}{2} \\ Square\text{ root both sides} \\ x-3\text{ = }\pm\sqrt{\frac{1}{2}} \\ x\text{ = 3 }\pm\text{ }\sqrt{\frac{1}{2}} \end{gathered}[/tex]Hence, the x-intercepts are:
[tex](\sqrt{\frac{1}{2}}\text{ + 3, 0\rparen, \lparen-}\sqrt{\frac{1}{2}}\text{ + 3,0\rparen}[/tex]y-intercepts
The y-intercepts are the values of y when x = 0
[tex]\begin{gathered} y\text{ = 2\lparen0-3\rparen}^2-\text{ 1} \\ =\text{ 2}\times9-1 \\ =\text{ 17} \end{gathered}[/tex]Hence, the y-intercept is (0, 17)
Maximum or minimum of the function
The given equation is in vertex form.
[tex]\begin{gathered} y\text{ = a\lparen x-h\rparen}^2\text{ + k} \\ Where\text{ \lparen h,k\rparen is the vertex} \end{gathered}[/tex]Hence, the minimum value of the function is (3,-1)
A teacher wants to track the number of books students have read each week,encouraging them to increase their reading throughout the school year. Which ofthe following graphs might be most effective to inspire the student?
We have to find which of the graph options is best to track the number of books that the students read each week and encourage them to increase them.
Option 1 (scatter plot): in this case, it is not useful in the sense that we can not compare the evolution in time of each student. We can only see the number of books per student for specific weeks.
Option 2 (time series): in this case, the attendance is not a variable of interest, so it is not suitable.
Option 3: A pie chart is only useful to compare proportions and percentages, and not track an evolution of a variable in time.
Option 4: This aggregation of the data in a Pareto only allows to compare the total number of books per week, but the evolution is not clear, as we sort the columns by the number of books instead of time.
Option 5: A time series with weeks in the x-axis and number of books in the y-axis let the teacher clearly see the evolution of books read in time. So this option is the most suitable.
Answer: Option 5 (time series)
what can you prove congruent from your given
Answer:
a. line OL bisects angle MLN
b. triangle MLO is congruent to triangle OLN
c. line OL proves that they are congruent through reflexive property.
Step-by-step explanation:
hope this helps!
What is the positive solution for x^3 + 3x - 9 = x -1 + 2x?
Given:
[tex]\begin{gathered} x^3+3x-9=x-1+2x \\ x^3+3x-9=3x-1 \\ x^3+3x-3x=-1+9 \\ x^3=8 \\ x^3=2^3 \\ \text{Therefore, x=2} \end{gathered}[/tex]Hence, the postive solution for the gven equation is x=2
(a)The perimeter of a rectangular garden is 306m.If the width of the garden is 69m, what is its length?Length of the garden: m (b)The area of a rectangular window is 6364cm2.If the length of the window is 86cm, what is its width?Width of the window: cm
Answer
The length of the garden = 84 m
Explanation
Part (a)
The given parameters are:
Perimeter of the rectangular garden = 306 m
The width of the garden = 69 m
The length of the garden = ?
Solution:
Using the formula for the perimeter of a rectangle:
[tex]\begin{gathered} Perimeter=2(Length+Width \\ \\ 306m=2(L+69m) \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \\ \frac{306m}{2}=\frac{2(L+69m)}{2} \\ \\ 153m=L+69m \\ \\ L=153m-69m \\ \\ L=84\text{ }m \end{gathered}[/tex]The length of the garden = 84 m
Part (b):
The given parameters are:
The area of the rectangular window = 6364 cm²
The length of the window = 86 cm
The width of the window = ?
Solution:
The width of the rectangular window can be calculated using the formula for the area of a rectangle.
[tex]\begin{gathered} Area=Length\times Width \\ \\ 6364cm^2=86cm\times W \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }86cm \\ \\ \frac{6364cm^2}{86cm}=\frac{86cm\times W}{86cm} \\ \\ W=74\text{ }cm \end{gathered}[/tex]The width of the window = 74 cm
Find the volume of the cylinder in terms of 3.14 and to the nearest tenth.
The volume formula of a cylinder is :
[tex]V=\pi r^2h[/tex]From the problem, we have :
r = 3 in and h = 2 in
Using the formula above, the volume will be :
[tex]\begin{gathered} V=\pi(3)^2(2) \\ V=3.14(9)(2) \\ V=56.52 \end{gathered}[/tex]The answer rounded to the nearest tenth is V = 56.5 in^3
Solve for x.
3(-3x-3)+2x+4=-33
Look at the system of equations shown.y = 3x + 7y = 2x + 8What is the x-coordinate of the solution to the system?Select one:10- 10O- 1o
We have a system of 2 equation (Eq):
y = 3x + 7 (Eq 1)
y = 2x + 8 (Eq 2)
To solve the system, we can match both equations.
3x + 7 = 2x + 8
3x - 2x = 8 - 7
x = 1
Find the slope, if it exists, of the line containg the pairs of pointsplease answer them all :(1. ( -4, -1 ) and ( 4, 4 )2. ( 0, 3 ) and ( 4, 0 )3. ( 0, 1 ) and ( 3, 0 )4. ( 7, 8 ) and ( -7, 8 )5. ( 1, 5 ) and ( -8, 5 )
The formula for determine the slope is given by
m = ( y2-y1)/(x2-x1) where ( x1,y1) and (x2,y2) are points on the line
m = ( 4 - -1)/(4 - -4)
Rewriting
m = ( 4+1)/( 4+4)
= 5/8
The slope is 5/8
Determine the inverse of the function by interchanging the variables and solving for y in terms of X
We are required to find the inverse of the function
The first step is to interchange the variable x for y
[tex]x=\frac{y}{2}-\frac{3}{2}[/tex]The next step is to make y the subject of the formula
[tex]\begin{gathered} x=\frac{y}{2}-\frac{3}{2} \\ \frac{y}{2}=x+\frac{3}{2} \\ \text{ Multiply the equation throughout by 2} \\ y\text{ = 2x + 3} \end{gathered}[/tex]The answer is y = 2x + 3
There were 24 dinner tables with 8 chairs at each table.Each dinner ticket cost $12.50. If 3/4 of thr dinner tables were full,how much money was raised from the dinner ticket sales?
we have the next information
24 dinner tables
each has 8 chairs
First we need to calculate 3/4 of the tables
24 mesas ----- 4/4=1
x ----- 3/4
x = the number of tabl
please help me find ALL of the questions this thing is asking :). Non helping (just to obtain points) questions will be reported.
i need to provide a two column proof. don’t except if you cannot do this. please
Statement Reason
angle P = angle S Given
angle P + angle Q = 180 Given
angle R + angle S = 180 Given
If we substitute angle P = angle S into angle R + angle S = 180, then
angle R + angle P = 180
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
B
Step-by-step explanation:
x + y = 180
co-interior
co-interior starts with C and x + y make a C shape (easier to remember)
Alan needs to manufacture a circular metal plate with a perimeter of `10pi` centimeters. If the allowed error tolerance in the perimeter is `+-1` centimeter, how close to the ideal radius must he control the radius of the plate?
A. `1/(5pi)`
B. `1/(10pi)`
C. `2/pi`
D. `1/(2pi)`
Answer: D. `1/(2pi)`
Your Welcome :)
The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
Define perimeter of circle.The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The area of a circle determines the space it takes up. A circle's diameter is equal to the length of a straight line traced through its center. Usually, it is stated in terms of units like cm or m.
Given data -
Perimeter of circular plate = 10[tex]\pi[/tex] cm
We know that perimeter of a circle is 2[tex]\pi[/tex]r
Therefore 10[tex]\pi[/tex] = 2[tex]\pi[/tex]r
r = 5 cm
The given error Alan can make is +-1 cm.
Minimum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] - 1
r = [tex]\frac{10\pi - 1 }{2\pi }[/tex]
r = 5 - [tex]\frac{1}{2\pi }[/tex]
Maximum radius is given by
2[tex]\pi[/tex]r = 10[tex]\pi[/tex] + 1
r = [tex]\frac{10\pi + 1 }{2\pi }[/tex]
r = 5 + [tex]\frac{1}{2\pi }[/tex]
The ideal radius Alan must control is [tex]\frac{1}{2\pi }[/tex] cm.
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Elizabeth wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box. 6 in 6.8 in
The wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
Dimension of the square base:
Side = 6.8 in.
Area of the base = 6.8 in. × 6.8 in.
A = 46.24 in.²
Dimension of the triangle:
Base = 6.8 in.
Height = 6 in.
Area of 1 triangle = 1/2 × 6.8 in. × 6 in.
A (triangle) = 20.4 in.²
Area of 4 triangles = 4 × 20.4 in.²
A' = 81.6 in.²
Total area of the square pyramid = A + A'
T = 46.24 in.² + 81.6 in.²
T = 127.84 in.²
Therefore, the wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
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Your question is incomplete. Please refer the content below:
Elizabeth wraps a gift box in the shape of a square pyramid.
The figure below shows a net for the gift box.
How much wrapping paper did she use?
The length of a 12 foot by 8 foot rectangle is increasing at a rate of 3 feet per second and the width is decreasing at 2 feet per second (a) How fast is the perimeter changing? (b) How fast is the area changing?
The rate of change of the perimeter of this rectangle is equal to 2 feet per second.
The rate of change of the area of this rectangle is equal to 20 feet per second.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.The rate of change for the perimeter of this rectangle is given by:
P = 2L + 2W
Differentiating with respect to t, we have:
dP/dt = 2dl/dt + 2dw/dt
Substituting the given parameters into the formula, we have;
dP/dt = 2(3) + 2(-2)
dP/dt = 6 - 4
dP/dt = 2 feet per second.
For the rate of change of the area of this rectangle, we have:
dA/dt = ldw/dt + wdl/dt
dA/dt = 8(-2) + 12(3)
dA/dt = -16 + 36
dA/dt = 20 feet per second.
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MATH HELP WILL MARK BRAINLEST
The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
In the question ,
it is given that ,
the equation is y = x² - 6x + 5
we need to write the equation in the vertex form ,
we know that the vertex form of the equation is
y = m(x − a)² + b , where (a,b) is the vertex .
On using the completing the square method for the equation,
y = x² - 6x + 5
Adding and subtracting 9 , in the equation
y = x² - 6x + 9 + 5 - 9
y = x² - 6x + 3² + 5 - 3²
y = (x - 3)² - 4 ....because (x - 3)² = x² - 6x + 3²
Therefore , The vertex form of the equation is y = (x - 3)² - 4 , the correct option is (b).
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in circle R, mCB=73° and mAD=57° what is M
The measure of the angle ∠CEB is 65°.
We are given a circle. The center of the circle is denoted by R. There are two chords, AB and CD. The point of intersection of the chords is E. The angles subtended by the arcs CB and AD are 73° and 57°, respectively. We have to find the measure of the angle ∠CEB. We can see that there is no direct relationship between the angles, but it is certain that the angle ∠CEB lies between the measures of angles subtended by the two arcs. So, we can write it in the form of an inequality. The measure of the angle ∠CEB is more than 57° but less than 73°. We can take the average value of these angles as an approximation. The average is (57° + 73°)/2 = 65°.
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