Answer:
x² + (y + 3)² = 25
Step-by-step explanation:
the centre (C) of the circle is at the midpoint of the diameter.
using the midpoint formula
midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
with (x₁, y₁ ) = P (3, 1 ) and (x₂, y₂ ) = Q (- 3, - 7 )
C = ( [tex]\frac{3-3}{2}[/tex] , [tex]\frac{1-7}{2}[/tex] ) = ( [tex]\frac{0}{2}[/tex] , [tex]\frac{-6}{2}[/tex] ) = (0, - 3 )
the radius r is the distance from the centre to either P or Q
using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = C (0, - 3 ) and (x₂, y₂ ) = P (3, 1 )
r = [tex]\sqrt{(3-0)^2+(1-(-3)^2}[/tex]
= [tex]\sqrt{3^2+(1+3)^2}[/tex]
= [tex]\sqrt{3^2+4^2}[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
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 ) = (0, - 3 ) and r = 5 , then
(x - 0 )² + (y - (- 3) )² = 5² , that is
x² + (y + 3)² = 25
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as
editing) and variable costs (such as printing). The one-time fixed costs will total $32,060. The variable costs will be $12.75 per
book. The publisher will sell the finished product to bookstores at a price of $21.50 per book. How many books must the
publisher produce and sell so that the production costs will equal the money from sales?
In linear equations x = 3,664 books are the production costs will equal the money from sales .
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.fixed cost = $32,060
variable cost = $12.75
here cost function
c(x) = fixed cost + x( variable cost )
c(x) = $32,060 + x($12.75) ................. 1
now revenue function
R(X) = (Selling price ).x
r(x) = ( 21.50)x .............2
where production cost is wqual to selling
c (X) = r (x)
32,0 60 + x($12.75) = ( 21.50)x
32,060 = ( 21.50)x - (12.75)x
32,060 = 8.75 x
x = 3,664 books
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The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 600 tickets. There is one $3,000 grand prize, two $500 second prizes, and thirteen $40 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.
The expected value for your profit is 2.53.
The probability is the number that indicates the likelihood that an event will occur and is defined as the ratio of favorable outcomes to all outcomes.
Given,
You can solve for the necessary anticipated value below.
There will be 600 tickets available for purchase overall.
So,
$ 5 each and sell go tickets
one $3,000 grand prize = ( 1/600) × 3000
two $500 second prizes = (2/600) × 500
thirteen $40 third prizes = (13/600) × 40
Any discrete variable X's anticipated value is calculated as:
E(x) = ( 1/600) × 3000 + (2/600) × 500 + (13/600) × 40 + (600-1-2-13/600).0-5
E(x) = 2.53
The expected value for your profit is 2.53.
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A small apartment has a 10ft by 10ft bedroom, a 5ft by 5ft bathroom, and a single multi-use 14ft by 18ft living room/kitchen. what is the total square footage (area) of the apartment?
The total square footage (area) of the apartment is 337 square feet.
It is given in the question that, In a small apartment:-
Dimensions of the bedroom = 10 ft by 10ft
Dimensions of the bathroom = 5 ft by 5 ft
Dimensions of the living room/kitchen = 14 ft by 18 ft
We have to find the total square footage (area) of the apartment.
We know that,
Area of square = [tex]side^2[/tex]
Hence,
Area of the bedroom = 100 square feet
Area of the bathroom = 25 square feet
Area of the living room/ kitchen = 212 square feet
Hence,
Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.
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K
Membership warehouse clubs offer shoppers low prices, along with rewards of cash back on club purchases. If the
yearly fee for a warehouse club membership is $100 and the reward rate is 4% on club purchases for the year, then the
linear equation y=100-0.04x models the actual yearly cost of the membership y, in dollars. Here x represents the
yearly amount of club purchases, also in dollars.
a) Determine the actual yearly cost of the membership if club purchases for the year
The actual yearly cost of the membership if club purchases for the year is $40
What is actual yearly cost of the membership of the club?
The annual membership cost of Membership warehouse clubs is modelled based on the fact that yearly fee is $100 and that 4% is given off purchases the member make in the course of year, hence, the actual yearly cost is modelled as shown below:
y=100−0.04x
y= actual yearly cost of the membership=unknown
x=cost of purchases in the year=$1,500
y=100-0.04($1500)
y=100-60
y=actual yearly cost of the membership =$40
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Full question:
Membership warehouse clubs offer shoppers low prices, along with rewards of cash back on club purchases. If the yearly fee for a warehouse club membership is $100 and the reward rate is 4%
on club purchases for the year, then the linear equation
y=100−0.04x models the actual yearly cost of the membership y, in dollars. Here x represents the yearly amount of club purchases, also in dollars.
a) Determine the actual yearly cost of the membership if club purchases for the year are $1500.
A television uses 1 unit of electricity every 10 hours.
A unit of electricity costs 9.8 p.
Calculate the cost of having a television turned on for 24 hours.
Answer:
Step-by-step explanation:
9.8 p = 10 hours
24 hours = ?
= 24 hours (9.8p)
10 hours
=23.92p
Leila says that 75% of a number will always be greater than 50% of any other number. complete one inequality to support leila's claim and one to show that she is incorrect. clear check support 75% of > 50% of refute 75% of < 50% of
The inequality for Leila claim is (0.75 × x) > (0.50 × y) and the support claim is x = 100 and y = 10 and that refutes the claim is x = 1 and y = 200
Inequality:
Inequality are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given,
Leila says that 75% of a number will always be greater than 50% of any other number.
Here we need to find the inequality and we also need to find one that supports Leila's claim and one to show that she is incorrect.
Let x and y be two numbers.
Leila says that 75% of a number will always be greater than 50% of any other number.
This means that the inequality is,
=> (0.75 × x) > (0.50 × y)
We know that,
75% of x = 0.75 × x
and
50% of y = 0.50 × y
So,
Numbers that support Leila's claim.
Let x = 100 and b = 10
=> 0.75 × x
=> 0.75 × 100 = 75
and
=> 0.50 × 10 = 5
As we know that, based in on the inequality,
=> 75 > 5
Hence, x = 100 and y = 10 support Leila's claim.
Similarly,
Numbers that refutes her claim.
Let x = 1 and y = 200
=> 0.75 × x
=> 0.75 × 1 = 0.75
and
=> 0.50 × 200 = 100
As we know that,
=> 0.75 < 100
Hence, x = 1 and y = 200 refutes Leila's claim.
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Heidi was riding her bike on a loop that is 7/8 mile long. she rode for 1/2 mile and then stopped to rest. she rode another 1/4 mile and then had a flat tire. how far does heidi have to wak her bike to complete the loop?
Heidi has to walk her bike for (1/8) mile to complete the loop.
Given that:-
Total distance of the loop = 7/8 mile
Distance Heidi rode on her bike before she stopped for rest = 1/2 mile
Distance Heidi rode on her bike after taking the rest = 1/4 mile.
We have to find the distance Heidi has to to walk to complete the loop because she had a flat tire.
Let the distance Heidi has to to walk to complete the loop because she had a flat tire is x miles.
We know that,
Total distance of the loop = Distance Heidi rode on her bike before she stopped for rest + Distance Heidi rode on her bike after taking the rest + distance Heidi has to to walk to complete the loop because she had a flat tire.
Hence, by adding the fractions, we get
7/8 = 1/2 + 1/4 + x
7/8 = (2+1)/4 + x
7/8 = 3/4 + x
7/8 - 3/4 = x
7/8 - 6/8 = x
1/8 mile = x
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If you have scores and you don't know the shape of their distribution, find the minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean? Round to two decimal places.
Using Chebyshev's Theorem, the minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.
What does Chebyshev’s Theorem state?When the distribution is unknown, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100\left(1 - \frac{1}{k^{2}}\right)[/tex].For this problem, we have that k = 1.8, hence the percentage is:
[tex]P = 100\left(1 - \frac{1}{1.8^{2}}\right) = 69.14[/tex]
The minimum proportion of scores that fall within 1.8 standard deviations on both sides of the mean is 69.14%.
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You read 105 pages of a novel over 7 days. What is the mean number of pages you read each day?
Answer:
15
Step-by-step explanation:
105/7
15
Hope It Helps
Solve the system:
c+12d=-66
-4c+3d=-42
Answer: c=6, d=-6
Step-by-step explanation:
c+12d=-66
-4c+3d=-42
(-4c+3d=-42)*4
-16c+12d=-168 ==> subtract this
c+12d=-66 ==> by this
-17c=-168-(-66) ==> subtract the top two equations
-17c=-168+66
-17c=-102
c=6
c+12d=-66
6+12d=-66
12d=-72
d=-6
I need help regarding a question about matrixes in math can someone please help?
Answer:
Hello,
x=5, y=-3, t=-17, z=-43
Step-by-step explanation:
[tex]\begin{bmatrix}2 & 1 \\3 & 1 \end{bmatrix}*\begin{bmatrix}x & 2z \\y & 3 \end{bmatrix}=\begin{bmatrix}7 &35 \\12 & 3t \end{bmatrix}\\\\\\\begin{bmatrix}2 & 1 \\3 & 1 \end{bmatrix}^{-1}=\begin{bmatrix}-1 & 1 \\3 & 2 \end{bmatrix}\\[/tex]
[tex]\\\\\begin{bmatrix}-1 & 1 \\3 & 2 \end{bmatrix}*\begin{bmatrix}2 & 1 \\3 & 1 \end{bmatrix}*\begin{bmatrix}x & 2z \\y & 3 \end{bmatrix}=\begin{bmatrix}-1 & 1 \\3 & 2 \end{bmatrix}*\begin{bmatrix}7 &35 \\12 & 3t \end{bmatrix}\\\\\\\begin{bmatrix}x & 2z \\y & 3 \end{bmatrix}=\begin{bmatrix}5 & -35+3t \\-3 & 105+6t\end{bmatrix}\\\\[/tex]
x=5
y=-3
t=-17
z=-43
An internet service provider is implementing a new program based on the number of connected devices in each household. Currently, customers are charged a flat rate of $175 per month. The new plan would charge a flat rate of $94 plus an additional $4.50 per device connected to the network. Find the number of devices, x, for which the cost of the new plan is less than the cost of the current plan
The device numbers should be less than 18.
Given, internet service provider is charging a rate of $175 per month.
The new plan would charge $94 plus an additional $4.50 per device connected to the network.
we need to find the number of devices for which the cost of the new plan is less than the cost of the current plan.
old plan = $175
New plan = $94 plus $4.50 per device
let us suppose 'x' devices can be connected.
so, 94 ₊ 4.5x < 175
4.5x < 175 ₋ 94
4.5x < 81
x < 81/4.5
x < 18
less than 18.
Hence there should be less than 18 devices connected for the new plan.
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Cathy is purchasing a DVD player and a TV at the local electronic store. The DVD player costs
$49.36, and the TV costs $705.20. If she plans to pay for them in 12 equal payments, then what is her
monthly cost?
The monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
What is debt?
It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We know the formula for the monthly payment:
It is given that:
Cathy is purchasing a DVD player and tv at the local electronic store.
The DVD player costs $49.36 and the tv cost $705.20.
If she plans for them in 12 equal payments,
Total cost(combining the cost of the DVD player and TV cost):
= $49.36 + $705.20
= $754.56
Per month payment = $754.56/12
Per month payment = $62.88
Thus, the monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
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Which statements are true about irrational numbers?
Select all that apply.
1. They are not real numbers.
2.Their decimal form contains a bar over one or more decimal numbers to show that they continue on infinitely.
3.They can be the square root of a non-perfect square.
4.They can be written as simple fractions.
5. Their decimal form contains an ellipsis, 3 dots, to show that they continue on infinitely.
Answer:
Step-by-step explanation:
the irrational number can't be represented to a fraction number, like pi and square root of 2 , e and so on, the third fourth choice are true
rational number and irrational number are included in real number, the second choice means the decimal numbers with circulating decimal, it is belong to rational number.
the fifth choice only be used to decimal number with circulating decimal, not the irrational number.
We know circle A is a congruent to circle B because
Since the radii of Circle A and Circle B are the same length, we know they are congruent.
What is defined as the congruent circles?Congruency is a geometric term that refers to objects that share the same size and shape (dimension).
Two circles, as well as other geometrical shapes such as triangles, quadrilaterals, or polygons, can be congruent. The center and radius of a circle are the two properties that define it. Because congruency is independent of location and then a circle remains the same irrespective of rotation and reflection, the radius of a circle determines its congruence.Again, because a radius 'r' is a constant (its value does not change) and is only equal to some other constant, all circles that have the same radius (and any value dependent on radius) are congruent to each other.For the given two circles, A and B are said to be congruent if the radii of both the circles are equal.
Thus, for circles to be congruent, the radii must be equal.
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Write the formula for the volume of a square prism, V= 1/3 s^2h, in terms of h. Then find the height h of a square prism with volume V=60cm^3 and side length s=6 cm.
The formula in terms of h is h = 3V/s^2 and the value of h is 5
How to write the formula in terms of h?The equation is given as
V = 1/3s^2h
Divide both sides of the equation by 1/3s^2
So, we have
h = 3V/s^2
The given parameters are
V = 60 and s = 6
So, we have:
h = 3 * 60/6^2
Evaluate
h = 5
Hence, the formula in terms of h is h = 3V/s^2 and the value of h is 5
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Use your calculator to work out the following and
write all the figures from your display.
a) √17.5
b) 2.3² + √5.6
5. What is the height of a triangle that has an area of 90 m² and a base with a length of 18 m?
Answer:
h = 10m
Step-by-step explanation:
[tex]A=\frac{bh}{2}[/tex]
[tex]90=\frac{18h}{2}[/tex]
[tex]18h=(90)(2)[/tex]
[tex]h=\frac{180}{18} =10[/tex]
Hope this helps
Can someone please help me?? :(
Answer: D (the bottom right)
Step-by-step explanation: The first problem stated is that Niki scored 20 points (positive) so you would point the arrow directed positively. Then she lost 10 points, which would be negative so the direction of the arrow would point back to a positive 10. Then lost another 25 points, leading to -15 (10+(-25)= -15
− 2|5 − 1| − 3 =− 11 Pls help
The lines mean absolute value.
Not sure what the question is, but both sides are equal to each other. -11=-11, so if the question is if both sides are equal, then it's true
The temperature was 71 degrees on thursday at 6 am. the temperature rose 4 degrees per hour and for several hours. at what time did the temperature reach 83 degrees
At 6 am temperature was 71 degrees and rises 4 degrees per hour then at 9 am temperature reach 83 degrees.
As given in the question,
On Thursday at 6 am temperature = 71 degrees
Rise in temperature = 4 degrees per hour
Temperature at
7 am = 71+ 4
= 75 degrees
8am = 75 + 4
= 79 degrees
9am = 79 +4
= 83 degrees
Therefore, at 6 am temperature was 71 degrees and rises 4 degrees per hour then at 9 am temperature reach 83 degrees.
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Find the circumference of a circle with radius, r = 9.5m.
Give your answer in terms of pi
The circumference of a circle with radius, r = 9.5m is 19π
What is circumference of circle?
The perimeter of a circle or ellipse is its circumference. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
What does a circle's circumference mean?
The complete length of a circle's arc is known as its circumference. The circumference of the circle is another name for it. The radius of the circle is the distance measured from any point on the circle to its center.
Given,
radius of the circle = 9.5m
The formula to calculate the circumference is -
C = 2πr
where r = radius of the circle
⇒ 2 × π × 9.5
⇒ 19π
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Show that the point (1,-1,2) is common to the lines which join (6,-7,0) to (16,-19,-4) and (0,3,-6) to (2,-5,10).
Answer:
The given point satisfies both equations of a line, hence is common to the two lines.
Step-by-step explanation:
Given two lines, one joining the points (6,-7,0) to (16,-19,-4), and the other joining the points (0,3,-6) to (2,-5,10), you want to show that the point (1, -1, 2) is common to those lines.
Equation of a lineThe equation of a line through points (x1, y1, z1) and (x2, y2, z2) can be written:
(x -x1)/(x2 -x1) = (y -y1)/(y2 -y1) = (z -z1)/(z2 -z1)
For the first pair of points, the equation of the line is ...
(x -6)/(16 -6) = (y +7)/(-19 +7) = (z -0)/(-4 -0)
(x -6)/10 = -(y +7)/12 = -z/4 . . . . . line 1
For the second pair of points, the equation of the line is ...
(x -0)/(2 -0) = (y -3)/(-5 -3) = (z +6)/(10 +6)
x/2 = -(y -3)/8 = (z +6)/16 . . . . . line 2
Point on the line?If the given point is on each of these lines, then it will satisfy each of the equations.
Line 1: (1 -6)/10 = -(-1 +7)/12 = -2/4 ⇒ -5/10 = -6/12 = -2/4 . . . true
The given point is on Line 1.
Line 2: (1)/2 = -(-1-3)/8 = (2+6)/16 ⇒ 1/2 = 4/8 = 8/16 . . . true
The given point is on Line 2.
The given point is common to both lines.
__
Alternate solution
For points A and B and parameter p, we can write the parameterized equation of each line as ...
(x, y, z) = A +p(B -A)
Using parameters t and s for the two lines, we get ...
Line 1: (x, y, z) = (6, -7, 0) +t(16 -6, -19 +7, -4 -0) = (6 +10t, -7 -12t, 0 -4t)
Line 2: (x, y, z) = (0, 3, -6) +s(2 -0, -5 -3, 10 +6) = (0 +2s, 3 -8s, -6 +16s)
A common point will be found where (x, y, z) for some value of t matches (x, y, z) for some value of s. We can find those values of s and t by solving simultaneous equations for any pair of the variables (x, y, z). The equations are ...
6 +10t = 2s-7 -12t = 3 -8s-4t = -6 +16sBy any of your favorite methods, these equations have the solution (t, s) = (-0.5, 0.5). The point the lines have in common is ...
(6 +10(-0.5), -7 -12(-0.5), 0 -4(-0.5)) = (6 -5, -7 +6, 2) = (1, -1, 2)
The common point to the two lines is (1, -1, 2).
Please help me with my math
please help with the question below asap !! thank you in advance !!
Are these good grades for middle school
Answer: kinda
Step-by-step explanation:
as long as you have a passing grade you will be fine, just work on the "F" :)
11x + 9x³ -8y + 5
14. What are the coefficients of the expression above?
15. What is the degree of the expression?
16. What is the constant of the expression?
17. How many terms are in the expression?
18. Write the expression listed above in standard form.
Problem 14
Answer: The coefficients are 11, 9, -8, and 5Reason: The coefficients are numbers to the left of the variables
======================================================
Problem 15
Answer: Degree = 3Reason: The degree is the largest exponent.
======================================================
Problem 16
Answer: Constant = 5Reason: The term without any variables attached is the constant.
======================================================
Problem 17
Answer: Four termsReason: The four terms are 11x, 9x^3, -8y, and 5
=======================================================
Problem 18
Answer: 9x^3 + 11x - 8y + 5Reason: Write the terms with the largest exponent first. Then have the exponents count down.
(6/7x-2/3)+3/5(5/8x-6/7)
Answer:
Step-by-step explanation:
1035x-992/840
45% of what number is 90?
I believe the answer is 200.
What is 54 as a percentage of 216?
%
Answer:
54 as a percentage of 216% is 116.64.
Step-by-step explanation:
100% of 54 is 54 so 54 x 2 would be 108. We have solved 200% of it now for the 16%. The percentage of 54 of 16% would be 8.64. Now add up all we have learned.
108 + 8.64 = 116.64
