The value of equation 1 = 8 and The value of equation 2 = 91 after substituting the given values.
Given the 2 equations,
1)[tex](x+5)^{2} -y[/tex] ; for x=-2 and y=1
2)3x+4[tex]y^{2}[/tex]; for x=-3 and y=5
Equation 1
⇒[tex](x+5)^{2} -y[/tex] ; for x=-2 and y=1
⇒[tex](-2+5)^{2}[/tex]-1 {substituting x=-2 and y=1 }
⇒[tex]3^{2}[/tex]-1
⇒9-1
⇒8
Equation 2
⇒3x+4[tex]y^{2}[/tex]; for x=-3 and y=5
⇒3(-3)+4[tex](5)^{2}[/tex] {substituting x=-3 and y=5 }
⇒-9+4(25)
⇒-9+100
⇒91
Therefore, The value of equation 1 = 8 and The value of equation 2 = 91 after substituting the given values.
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in the sketch below abc is not drawn to scale constuct abc next to its sketch below
The letter A is not drawn to scale in the sketch below. construct ABC next to its below-listed sketch The amount of force applied over a specific distance is referred to as work. Since the problem already specifies the force's value and the length of the distance it is exerted across, the quantity of labor completed requires multiplying these two numbers. As demonstrated below:
work, in physics, measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement.
Work: Force times Distance
Work = 250 J x 50 N * 5 m
Work = 250 J
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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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What is 90.5-7.83? Please show your work too! Thanks.
Use integration and trigonometric substitution to find the area enclosed by the ellipse: x 2 4 y 2 81 = 1 .
The area enclosed by the ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] is 60 square units.
The general form of the equation of ellipse is [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
Given the equation of ellipse is, [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex]
⇒ [tex]\frac{x^2}{2^2}+\frac{y^2}{9^2}=1[/tex]
That is, a = 2 and b = 9
Now, [tex]\frac{y^2}{9^2} = 1 -\frac{x^2}{2^2}[/tex]
⇒ [tex]y=\frac{9}{2} \sqrt{4-x^2}[/tex]
Area enclosed by the ellipse = 4 x Area of ellipse in the first quadrant
Therefore, Area of ellipse in the first quadrant, A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-x^2}} \, dx[/tex]
Using Substitution ,x = 2cosθ, then dx = -2sinθdθ and x = 0⇒ θ = π/2 and x = 2⇒ θ = 0
A = [tex]\int\limits^a_0{\frac{9}{2} \sqrt{4-4cos^2\theta}} \, dx[/tex]
= [tex]\int\limits^2_0{\frac{9}{2}\times2 \sqrt{1-cos^2\theta}} \, dx[/tex]
= [tex]\int\limits^2_0{9 sin^2\theta} \, dx[/tex]
= [tex]\int\limits^0_\frac{\pi}{2} {9 sin^2\theta} (-2sinx)\, d\theta[/tex]
= [tex]\int\limits^\frac{\pi}{2} _0{18 sin^3\theta} \, d\theta[/tex]
= [tex]\int\limits^\frac{\pi}{2} _0{18 (\frac{3sin\theta-sin3\theta}{4} )} \, d\theta[/tex]
= [tex]\frac{9}{2} \int\limits^\frac{\pi}{2} _b {3sin\theta} \, d\theta -\frac{9}{2} \int\limits^\frac{\pi}{2} _0 {sin3\theta} \, d\theta[/tex]
= 27/2 x (-cosθ) - 9/6 x (-cos3θ) | θ = 0 to θ = π/2
= 15 square units.
Therefore, the area enclosed by ellipse [tex]\frac{x^2}{4}+\frac{y^2}{81}=1[/tex] = 4 x A = 4 x 15 = 60 square units.
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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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You need to buy a 20-foot length of 15-wide carpet that costs $29.50 per square yard. How much will this cost?
Please include steps!!
The cost of the carpet will be $983.33
Calculating costFrom the question, we are to calculate how much the carpet will cost
From the given information,
The carpet has a length of 20 feet
and a width of 15 feet
First, we will covert the dimension to yard
NOTE: 1 foot = 1/3 yards
Thus,
20 feet = 20/3 yards
and
15 feet = 15/5 yards = 5 yards
Now, we will calculate the area of the carpet
Using the formula,
Area = Length × Width
Area of the carpet = 20/3 × 5 square yard
Area of the carpet = 33.33 square yard
Now, we have that
The carpet costs $29.50 per square yard
∴ The cost of the carpet = 20/3 × 5 × $29.50
The cost of the carpet = $ 983.33
Hence, the cost of the carpet will be $983.33
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The number of students in the four sixth-grade classes at Northside School are 36,19,34, and 21. Use properties to find the total number of students in the four classes. PLEASE HELP I DONT UNDERSTAND!
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
Rewrite 8x8x8 using exponents.
Answer:
8^3
Step-by-step explanation:
there are three 8s soo all u do is count the number and then how many of that same number you can put into an exponent
Pia poured 1/4 pint of milk into an empty mug. The milk filled 2/3 of the mug.
How many pints of milk will fill an empty mug of the same size?
3/8 pints of milk will fill an empty mug of the same size.
In this question, we have been given Pia poured 1/4 pint of milk into an empty mug.
The milk filled 2/3 of the mug.
We need to find the pints of milk that will fill an empty mug of the same size.
Let 'm' pints of milk will fill an empty mug of the same size.
From given data, we get proportion.
⇒ (1/4) / (2/3) = m / 1
We simplify above equation to find the value of m.
⇒ (2/3) m = 1/4
⇒ m = (1/4) × (3/2)
⇒ m = 3/8
Therefore, 3/8 pints of milk will fill an empty mug of the same size.
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Solve the conjunction and graph it’s solution set
y = -1 and y≥ 3
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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help meeeeeeeeeeeeee
======================================================
Explanation:
To find the inverse, we swap x and y, then solve for y.
y = 2x-3
x = 2y-3
x+3 = 2y
2y = x+3
y = (x+3)/2
y = x/2 + 3/2
y = (1/2)x + 3/2
This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.
--------------
Another approach:
Since we're given a list of multiple choice answers, we can rule out the non-answers.
Plug x = 0 into the first equation of choice A. It leads to y = 2
That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.
This allows us to rule out choice A. Choices B and C are similar stories.
Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.
Answer:
Step-by-step explanation:
Algorithm for deriving the formula of the inverse function
Step 1. In the formula for the original function, replace the notation of the argument and the value:
Step 2. From the resulting formula, express y(x).
Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.
[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]
[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]
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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Givien g(x) = -3x-5 , find g(4)
Answer: g(4)=-17
Step-by-step explanation:
You just plug in 4 into x.
-3(4)-5
-12-5
=17
Answer:
g(4) = -17
Step-by-step explanation:
Hello!
Substitute 4 for x in the equation.
Evaluateg(x) = -3x - 5g(4) = -3(4) - 5g(4) = -12 - 5g(4) = -17g(4) is -17.
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
please help me as soon as possible with this
Part A: The student was supposed to divide before subtracting
Part B: The student was supposed to simplify the parentheses before finding the exponents
Part C: The simplification of the expression gives -16.
From the question, we are to simplify the given expression
The given expression is
(∛64 - 16 ÷ 2)(2 - 4)²
Part A:
The mistake the student made was not applying the PEMDAS rule
P - Parentheses
E - Exponent
M - Multiplication
D - Division
A - Addition
S - Subtraction
Since division comes before subtraction, the student was supposed to divide before subtracting
Part B:
The student mistake was trying to simplify the exponent before simplifying the parentheses. The student was supposed to simplify the parentheses before finding the exponents.
Part C:
Simplifying the expression
(∛64 - 16 ÷ 2)(2 - 4)²
Simplify the cube root
(4 - 16 ÷ 2)(2 - 4)²
Divide
(4 - 8)(2 - 4)²
Simplify the parenthesis
(-4)(-2)²
Simplify the exponent
(-4)(4)
Evaluating
-16
Hence, the simplification of the expression gives -16.
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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
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" :)
12. Jeremy has 3 pounds of ground beef to make hamburgers. How many 1/3-pound hamburgers can he make?
Answer: He can make 9 hamburgers.
Step-by-step explanation:
one hamburger can be made by 1/3 of beef,
so according to ratio and proportions ,
1 beef can make 3 hamburgers,
hence 3 pound of beef can be used to make
=3*3
=9 hamburgers
hence,
He can make 9 hamburgers.
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Answer:1
Step-by-step explanation: firstly , divide 3 by 1\3 then 3÷1\3=1
When drawing a line, use
_____ to show that the line continues endlessly in both directions. (Fill in the blank)
when drawing a line use arrows to show that the line continues endlessly in both directions.
When the same number is added to the numerator and denominator of 5/7, the result is 17/23. what is that number?
The number added to the numerator and the denominator is 2/3.
It is given in the question that when the same number is added to the numerator and denominator of fraction 5/7, the result is 17/23.
We have to find the number added to the numerator and the denominator.
Let the number be x.
Hence, according to the data given in the question, we get,
(5 + x)/(7 + x) = 17/23
By cross - multiplication, we get
23(5 + x) = 17 (7 + x)
Opening the bracket according to the distributive property of addition and multiplication, we get,
115 + 23x = 119 + 17x
23x - 17x = 119 - 115
6x = 4
x = 4/6
x = 2/3
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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).
What is 8.7x3.9 in a step by step
Your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon on this winding road. to be sure you don't run out of gas, you never want to have less than 1 gallon in the tank. you start with a full tank of gas. will you need to stop for gas during the first day's drive? explain how you know, and show your work.
If you had to drive for more than 300 miles for the first day you need to stop for gas fill up.
What is unitary method ?Unitary method is a mathematical tool for finding the value of single unit then deriving the given units according to the question.
According to the given question your car's gas tank holds 13 gallons, and you expect to get about 25 miles per gallon.
Given that you never want to run out of gas to not face this issue you always keep 1 gallon of gas in the tank.
So when you fill your tank completely you fill for 12 gallons of gas because 1 gallon is already there.
Also given that the car can go 25 miles per gallon.
So, for 12 gallons of gas you can go (25 × 12 ) miles which is
= 300 miles.
If you had to drive for more than 300 miles then you need to stop for gas in first day's drive.
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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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Which numbers in Set A = {5, 9, 12, 14, 18} are elements of both Set B and Set C, shown below? Set B = {even numbers} Set C = {multiples of 3}
The numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.
How to illustrate the information?It should be noted that even numbers can be divided by 2.
The multiple of 3 in the numbers are 12 and 18 that can be divided by 2 as well.
Therefore, the numbers in Set A = {5, 9, 12, 14, 18} that are elements of both Set B and Set C, shown below Set B = {even numbers} Set C = {multiples of 3} will be 12 and 18.
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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
y(a-b)=c(y+a) what's the answer
Linear equation: a, b, c, and r are real numbers (and if a, b, and c are not all equal to 0)
then ax + by + cz = r is called a linear equation in three variables. (The
“three variables” are the x, the y, and the z.)
The numbers a, b, and c are called the coefficient of the equation. The
number r is called the constant of the equation
y(a-b)=c(y+a)
ya-yb=cy+ca
ya-yb-cy=ca
y(a-b-c)=ca
[tex]y=\frac{ca}{a-b-c}[/tex]
case 1:
if either C and a are zero the y is zero,
case 2:
if
[tex]c\neq 0 \\a\neq 0\\y\neq 0[/tex]
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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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