The number of students who voted for each mascot is given as follows:
Tigers: nT = pT/100 x 480.Cheetahs: nC = pC/100 x 480.Then the difference is given as follows:
nT - nC.
How to obtain the difference?The difference between the two amounts is obtained applying the proportions in the context of the problem.
The circle graph gives the percentage of each type of vote.
Hence the amounts relative to each type of vote are given as follows:
Tigers: nT = pT/100 x 480.Cheetahs: nC = pC/100 x 480.In which:
pT is the percentage of students that voted Tigers on the circle graph.pC is the percentage of students that voted Cheetahs on the circle graph.Missing Information
The problem is incomplete, hence the general procedure is given to solve the problem.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
If h(z)=2z^(4)-10z^(3)+20z^(2)-25z+3, use synthetic division to find h(2). Submit
Using synthetic division, h(2) = -9.
To find h(2) using synthetic division, we will divide the polynomial h(z) by (z-2). The steps are as follows:
1. Write the coefficients of the polynomial in a row: 2 -10 20 -25 3
2. Write the value of z we are dividing by in the upper left corner: 2 | 2 -10 20 -25 3
3. Bring down the first coefficient: 2 | 2 -10 20 -25 3
-------------------
2
4. Multiply the first coefficient by the value of z and write the result below the second coefficient: 2 | 2 -10 20 -25 3
-------------------
2 4
5. Add the second coefficient and the result from step 4: 2 | 2 -10 20 -25 3
-------------------
2 -6
6. Repeat steps 4 and 5 for the remaining coefficients: 2 | 2 -10 20 -25 3
-------------------
2 -6 8 -6
7. The last number in the bottom row is the remainder: 2 | 2 -10 20 -25 3
-------------------
2 -6 8 -6 -9
8. The value of h(2) is the remainder, so h(2) = -9.
Therefore, the answer is h(2) = -9.
You can learn more about synthetic division at
https://brainly.com/question/29638766
#SPJ11
Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
In the given figure the equation m∠MRS + m∠MRO = 180° is the postulate describing the linear pair of angles.
What is an angle?The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.
It is given that -
∠MRS ≅ ∠MRO
Now, what that means is that ∠MRS is congruent to ∠MRO.
Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -
m∠MRS = m∠MRO = 90°
Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.
m∠MRS + m∠MRO = 180°
It is seen that the angles form a linear pair and lie on the same plane.
Therefore, the correct postulate is linear pair.
To learn more about angle from the given link
https://brainly.com/question/2046046
#SPJ1
Owen is writing a program that will lock his computer for one hour if the incorrect password is entered more than five times. This set of instructions is an example of GIVING BRAINLIEST AND 25 POINTS
A a loop
B an algorithm
C debugging
D logical reasoning
The correct option is B an algorithm. If the wrong password is put in more than five times, Owen's computer will lock for an hour. To prevent this, he is building a programme. An illustration of a "algorithm" is this collection of instructions.
Explain about the algorithm?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms operate as a detailed sequence of instructions that carry out prescribed operations sequentially.
All aspects of information technology leverage algorithms extensively. A simple technique that resolves a recurring issue is typically referred to as an algorithm in computer science and math. Algorithms are essential to automated systems because they serve as specifications for processing data.An initial input and a list of instructions are used by algorithms. The input, which can be described as either words or numbers, is the first batch of information required to make judgements. The input data is subject to a number of calculations or instructions.Know more about algorithm
https://brainly.com/question/30637743
#SPJ1
If the velocity of an orbiting body were increased, its orbital path would change
into a parabola or hyperbola. If this were to happen, what would happen to the
object and its gravitational pull of the Sun?
The gravitational pull of the Sun on the object would decrease as the distance between them increased.
What is the gravitational pull?If the velocity of an orbiting body were increased, its orbital path would change from an elliptical orbit to a parabolic or hyperbolic orbit, depending on the extent of the increase in velocity.
The amount of gravitational pull on the object would decrease as the distance between the object and the Sun increased. This is because gravitational force decreases with distance according to the inverse-square law.
In summary, if the velocity of an orbiting body were increased to the point where its orbital path changed into a parabolic or hyperbolic orbit, the object would eventually escape the Sun's gravitational pull and move away from it in a straight line.
Learn more about gravitational pull:https://brainly.com/question/13467280
#SPJ1
Two  parallel lines, M and N Are cut by the transversal as shown suppose M1 equals 70 
The measure of angle 2 is 70° and the measure of angle 3 is also 70°°.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
From the given information ∠1 and ∠3 are pairs of alternate interior angles.
Therefore, m∠1 = m∠B = 70°.
We also know that the vertically opposite angles are equal,
Here ∠1 and ∠2 are vertically opposite angles,
Therefore, m∠1 = m∠2 = 70°.
learn more about transversals here :
https://brainly.com/question/28983284
#SPJ9
Help algebra 2 please answer 8 its urgent
The time it takes for the bacteria to reach 1,000,000 is given as follows:
t = 164.5 minutes.
How to obtain the time needed?The number of bacteria after t minutes is given by the exponential function presented as follows:
P(t) = 1000e^(0.042t).
The population will reach 1,000,000 when:
P(t) = 1,000,000.
Hence the time needed is obtained solving the equation as follows:
1,000,000 = 1000e^(0.042t).
e^(0.042t) = 1,000,000/1,000
e^(0.042t) = 1000.
The inverse operation regarding the exponent e is the natural logarithm, hence we can isolate t as follows:
0.042t = ln(1000)
t = ln(1000)/0.042
t = 164.5 minutes.
More can be learned about exponential functions at https://brainly.com/question/30113628
#SPJ1
find tan a if necessary write answer as fraction
One year, an estimated 6,955 sandhill cranes migrated in March. The next March, an estimated 3,480 sandhill cranes migrated. To the nearest percent, what is the percent change in the number of migrating cranes from the first March to the next? Decreases should be negative numbers and increases should be positive numbers. Do not include the percent in your answer
Rounding to the nearest percent, we get that the percent change in the number of migrating cranes from the first March to the next is approximately -50%.
How is a percentage calculated?To calculate the percentage, we must first divide the amount by the total value and then multiply the result by 100.
To find the percent change in the number of migrating cranes from the first March to the next, we can use the formula:
percent change = ((new value - old value) / old value) × 100%
where the old value is the number of migrating cranes in the first March and the new value is the number of migrating cranes in the next March.
Substituting the given values, we get:
percent change = ((3480 - 6955) / 6955) × 100%
Simplifying, we get:
\percent change = (-3475 / 6955) × 100%
percent change ≈ -50%
Rounding to the nearest percent, we get that the percent change in the number of migrating cranes from the first March to the next is approximately -50%.
To know more about percentage visit:
https://brainly.com/question/29306119
#SPJ1
A stadium has 10,500 seats and eight VIP boxes. The stadium is divided into 12 equal sections to premium sections and 10 standard sections. A seat at the premium section cost $48 per game. AC at the standard section cost $27 per game.  how many more seats are there in each section? If all the seats in the premium section are sold out for a game how many will the stadium get from those tickets sales? PLEASE HELP 44 POINTS!
Answer:
There are 875 seats. The stadium got $168,000 from the tickets.
Step-by-step explanation:
So there is more than one question so let's break them down one by one
1). How many seats are there in each section? So the stadium is divided into 12 sections and 8 are VIP boxes so 12 - 8 = 4 so there are 4 non-VIP sections. Now to find out how many seats are in each section we need to divide the number of seats by the number of sections which would be 10,500 ÷ 12 = 875.
2). If all the seats in the premium section are sold out for the game how many will the stadium get from those ticket sales? So first we need to find out how many seats there are in the premium section, we already know that there are 4 premium sections and we also know that there are 875 seats in each section. Multiply the number of sections by the number of seats 4 x 875 = 3,500 now multiply the number of seats by the cost of the seat 3,500 x $48 = $168,000
So the answers are $168,000 and 875 seats
Hope this helped :)
2 A DVD rental company charges $10 per month plus $0.75 per rental. Andy wants to spend no more than $25.00 per month on DVD rentals.
Select the inequality that represents how many DVDs Andy can rent in one month that satisfies this condition. The number of rentals in a month is represented by n.
The inequality that represents how many DVDs Andy can rent in one month that satisfies this condition is 10 + .75n ≤ 25
The correct answer choice is option B
Which inequality represents how many DVDs Andy can rent in one month?Cost of rental per month = $10
Additional cost = $0.75
Number of DVD's rented = n
Total amount Andy want to spend ≤ $25
The inequality:
10 + 0.75n ≤ 25
subtract 10 from both sides
0.75n ≤ 25 - 10
0.75n ≤ 15
divide both sides by 0.75
n ≤ 15 / 0.75
n ≤ 20
Ultimately, Andy can rent no more than 20 DVD's in a month.
Read more on inequality:
https://brainly.com/question/25275758
#SPJ1
how many different 3 digit numbers can be formed from 1,3,5,7,9 if each number formed is greater than 300? distinguishable permutations
There are a total of 28 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. This can be found by using the formula for distinguishable permutations.
There are a total of 5 different 3-digit numbers that can be formed from the numbers 1,3,5,7,9 if each number formed is greater than 300. These numbers are 315, 357, 375, 397, and 359. This can be found by using the formula for distinguishable permutations, which is n!/(n-r)!, where n is the total number of items and r is the number of items chosen. In this case, n is 5 (the numbers 1,3,5,7,9) and r is 3 (the number of digits in each number formed).
The formula for distinguishable permutations is:
n!/(n-r)!
= 5!/(5-3)!
= 120/2
= 60
Therefore, there are a total of 60 different 3-digit numbers that can be formed from the number 1,3,5,7,9. However, we need to subtract the numbers that are less than 300, which are the numbers formed from the digits 1 and 3 in the hundreds place. There are 2 numbers in the hundreds place (1 and 3) and 4 numbers in the tens and ones place (3,5,7,9), so there are a total of 2*4*4 = 32 numbers less than 300. Subtracting these from the total gives us:
60 - 32 = 28
To learn more about permutations here:
https://brainly.com/question/1216161#
#SPJ11
There are five cities in a country, and two are connected with one road that goes straight between them. How many roads would be in this country if there were 6 cities? 7 cities? And N cities? PLEASE SOLVE 20 POINTS!
For 6 cities, the number of roads would be 9. This is because each city must be connected to every other city, and there are 5 pairs of cities that need to be connected, which means 5 roads.
What is road?Roads are a form of transportation infrastructure consisting of a prepared surface for vehicles to travel on. They are typically made from asphalt or concrete and are designed to provide a safe and efficient means of travel.
Then, the remaining 4 cities need to be connected, which means 4 more roads for a total of 9.
For 7 cities, the number of roads would be 12. This is because each city must be connected to every other city, and there are 6 pairs of cities that need to be connected, which means 6 roads. Then, the remaining 5 cities need to be connected, which means 5 more roads for a total of 12.
For N cities, the number of roads would be equal to N(N-1)/2. This is because each city must be connected to every other city, and there are N(N-1)/2 pairs of cities that need to be connected. For example, if N = 10, then 10 × 9 = 90 pairs of cities need to be connected, which means 90 roads.
To learn more about road
https://brainly.com/question/30174321
#SPJ1
4. [10 pts) 25 participants enter a sushi-making competition! Each of them must make 4 rolls with different proteins: a salmon roll, a tuna roll, a shrimp roll, and a crab roll, for a total of 100 rolls made in the competition. All of the rolls are distinguishable, even if they have the same protein (ex. a salmon roll is distinguishable from all other salmon rolls, as well as all the other rolls with different protein). According to the competition rules, salmon and tuna rolls are always made with white rice, while shrimp and crab rolls are always made with brown rice. The judges select a sushi roll uniformly at random from the 100 rolls. Without putting it back, they select a second roll uniformly at random from the remaining 99 rolls. What is the probability that both of the rolls are made by the same participant, or both have the same protein, or one has white rice and one has brown rice?
50 possible combinations
The probability that both of the rolls are made by the same participant is 25/99, since there are 25 participants and the second roll must be chosen from the remaining 99 rolls. The probability that both rolls have the same protein is 4/99, since there are 4 types of proteins and the second roll must be chosen from the remaining 99 rolls. Lastly, the probability that one roll has white rice and one roll has brown rice is 50/99, since there are 50 possible combinations of white and brown rice and the second roll must be chosen from the remaining 99 rolls.
Learn more about probability
brainly.com/question/30034780
#SPJ11
Since (84/85, -13/85) is on the unit circle, with the center of
the origin, the point (a, b) in QII is also on
the circle.
(a,b) = ( , )
The point (a, b) in QII that is also on the unit circle is (-84/85, 13/85).
So, (a,b) = (-84/85, 13/85).
Since the point (84/85, -13/85) is on the unit circle with the center at the origin, the point (a, b) in QII is also on the circle if it satisfies the equation of the unit circle centered at the origin, which is x^2 + y^2 = 1.
In QII, the x-coordinate is negative and the y-coordinate is positive. So, we can write (a, b) as (-a, b), where a > 0 and b > 0.
Substituting (-a, b) into the equation of the unit circle, we get:
(-a)^2 + b^2 = 1
a^2 + b^2 = 1
Since (84/85, -13/85) is on the unit circle, we can use the Pythagorean theorem to find the value of a and b:
(84/85)^2 + (-13/85)^2 = 1
a^2 = (84/85)^2 = 7056/7225
b^2 = (-13/85)^2 = 169/7225
Taking the square root of both sides, we get:
a = sqrt(7056/7225) = 84/85
b = sqrt(169/7225) = 13/85
Therefore, the point (a, b) in QII that is also on the unit circle is (-84/85, 13/85).
So, (a,b) = (-84/85, 13/85).
Learn more about Unit circle.
brainly.com/question/11987349
#SPJ11
Paula bought $12.74$12.74 worth of $0.49$0.49 stamps and $0.21$0.21 stamps. The number of $0.21$0.21 stamps was six less than the number of $0.49$0.49 stamps. Solve the equation 0.49s+0.21(s−6)=12.740.49�+0.21(�-6)=12.74 for s�, to find the number of $0.49$0.49 stamps Paula bought.
The number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.
To solve the equation 0.49s + 0.21(s - 6) = 12.74 for s, we can multiply both sides by 100 to get:
49s + 21(s - 6) = 1274
Now, we can move the 21(s - 6) term to the left side of the equation and the 49s term to the right side of the equation. To do this, we will subtract the 49s from both sides of the equation, which yields:
21(s - 6) = 1274 - 49s
Next, we can divide both sides of the equation by 21 to isolate the (s - 6) term, resulting in:
(s - 6) = 1274 - 49s / 21
Finally, we can add 6 to both sides of the equation to solve for the number of $0.49$ stamps that Paula bought:
s = (1274 - 49s / 21) + 6
Therefore, the number of $0.49$ stamps Paula bought is s = (1274 - 49s / 21) + 6.
Learn more about equation
brainly.com/question/29657992
#SPJ11
Please answer fast !
Question 5(Multiple Choice Worth 2 points)
(Identifying Functions LC)
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
A mapping diagram with one circle labeled x values containing values negative 3, negative 1, 1, 3, and 5 and another circle labeled y values containing values 0, 2, and 5 and arrows from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5.
Is the relation a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
The correct answer is "No, because for each input there is not exactly one output".
What are Functions?A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.
The relation is not a function because for the input value of 1, there are two possible output values: 0 and 2. In a function, each input can have only one output value. However, in this relation, the input value of 1 is associated with two different output values, so it violates the definition of a function. Therefore, the correct answer is "No, because for each input there is not exactly one output".
To learn more about Functions from the given link
https://brainly.com/question/22340031
#SPJ1
Val rented a bicycle while she was on vacation. She paid flat rental fee for 55. 0
The equation that can be used to determine the number of days is $123 = $55 + $8.50d
What is the equation?An equation is an expression that has an equal to sign. A linear equation is an equation that has a single variable raised to the power of one. The form of a linear equation is:
y = mx + b
Where:
m = slope b = interceptThe form of the linear equation that can be used to determine the number of days is:
Total cost = flat fee + (cost per day x number of days)
$123 = $55 + ($8.50 x d)
$123 = $55 + $8.50d
d = ($123 - $55) / 8.50
d = 8 days
Here is the complete question:
Val rented a bicycle while she was on vacation. She paid a flat rental fee of $55.00, plus $8.50 each day. The total cost was $123. Write an equation you can use to find the number of days she rented the bicycle.
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
A parabola has x-intercepts -2 and -8, and has vertex (-5,-18). Determine the equation of this parabola in the form y=a(x-r)(x-s) Consider the function f(x)=4x^3+1. a) Find the derivativo of f. Answer f’(x)= b) Compute the derivative of f at x=1. Answer f’(1)=
c) Deterine the equation of the tangent line to the curve y=f(x) at the point (1,5).
a) The derivative f'(x) is 12x².
b) The amount of f'(1) is 12.
c) The equation of the tangent line is 12x - 7.
a) To find the derivative of f(x), we can use the power rule for each term. The power rule states that for any function f(x) = xⁿ, the derivative f'(x) = nx^(n-1). So for f(x) = 4x³ + 1, Thus, the derivative f'(x) = 12x².
b) To compute the derivative of f at x=1, we simply plug in x=1 into the derivative equation we found in part a. So f'(1) = 12(1)² = 12.
c) To determine the equation of the tangent line to the curve y=f(x) at the point (1,5), we use the point-slope form of a line, which is y-y1 = m(x-x1), where m is the slope of the line and (x1,y1) is the point the line passes through. The slope of the tangent line is the derivative of f at x=1, which we found in part b to be 12. So the equation of the tangent line is y-5 = 12(x-1), or y = 12x - 7.
Learn more about the derivative: https://brainly.com/question/30365299
#SPJ11
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times cosine theta plus radical 3 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of their spring can be represented by the function g of theta equals 1 minus sine squared theta plus radical 3 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.
The graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).
What is Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.
Part A:
To find when the pogo stick's spring will be equal to its non-compressed length, we need to solve for when f(θ) = 0.
f(θ) = 2cos(θ) + √3 = 0
2cos(θ) = -√3
cos(θ) = -√3/2
The solutions for θ in the interval [0, 2π) where cos(θ) = -√3/2 are θ = 2π/3 and θ = 4π/3.
Part B:
If we double the angle, θ becomes 2θ, and the function becomes:
f(2θ) = 2cos(2θ) + √3
Using the double angle formula for cosine, we can rewrite this as:
f(2θ) = 2(2cos²(θ) - 1) + √3
f(2θ) = 4cos²(θ) - 2 + √3
Substituting cos(θ) = -√3/2, we get:
f(2θ) = 4(-3/4) - 2 + √3
f(2θ) = -3 + √3
So the solutions for 2θ in the interval [0, 2π) where f(2θ) = 0 are:
2θ = π/6 and 2θ = 11π/6
Dividing by 2, we get the solutions for θ:
θ = π/12 and θ = 11π/12
These solutions are different from the solutions in Part A, and the graph of f(θ) is shifted and stretched when compared to the graph of f(2θ).
Part C:
To find when the lengths of the springs are equal, we need to solve the equation f(θ) = g(θ).
2cos(θ) + √3 = 1 - sin²(θ) + √3
2cos(θ) = 1 - sin²(θ)
Using the identity sin²(θ) + cos²(θ) = 1, we can rewrite this as:
2cos(θ) = cos²(θ)
cos(θ)(cos(θ) - 2) = 0
The solutions for θ in the interval [0, 2π) where the lengths of the springs are equal are:
θ = 0, θ = π/3, θ = 2π/3, θ = π, θ = 4π/3, θ = 5π/3
We can check that f(θ) = g(θ) at each of these values.
To learn more about Trigonometry from the given link
https://brainly.com/question/24349828
#SPJ1
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
The constant proportionality between the x-coordinates and y-coordinates of these four points is 12.
What is Proportionality?
Proportionality refers to the relationship between two quantities that change in a consistent and predictable way. In a proportional relationship, when one quantity changes, the other quantity changes in a constant ratio or proportion to the first.
Assuming that you want to find the constant proportionality between the x-coordinates and y-coordinates of these four points:
First, we can calculate the ratios of the y-coordinates to the x-coordinates for each point:
For (3,36): y/x = 36/3 = 12
For (5,60): y/x = 60/5 = 12
For (6,72): y/x = 72/6 = 12
For (7,84): y/x = 84/7 = 12
We can see that the ratios are all equal to 12. Therefore, the constant proportionality between the x-coordinates and y-coordinates of these four points is 12.
Note that if you had asked for the constant proportionality between the differences in the y-coordinates and the differences in the x-coordinates of these points, the answer would be different. That constant proportionality is known as the slope of the line passing through these points.
To learn more about Proportional Relationship from the given link
https://brainly.com/question/28777033
#SPJ1
21 How many solutions does the equation 2 + 6(x-4)= 3x - 18 + 3x have? A) O B 1 (c) 2 D) Infinite
I am needing some help with this
The volume of the rectangular pyramid is 1200 m³, the volume of the oblique cone is 5890 ft³ while the volume of the triangular prism is 321.75 ft³
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
a) The volume of the rectangular pyramid is:
Volume = (1/3) * area of base * height
Substituting:
Volume = (1/3) * (15 m * 12 m) * 20 m = 1200 m³
b) The volume of the oblique cone is:
Volume = (1/3) * π * radius² * height
but radius = 30 ft / 2 = 15 ft,
Substituting:
Volume = (1/3) * π * 15² * 25 = 5890 ft³
The volume of the cone is 5890 ft³
c) The volume of the triangular prism is:
Volume = area of base * height
Substituting:
Volume = (1/2 * 9 ft * 5 ft) * 14.3 ft = 321.75 ft³
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Zational Equations (Level 1) eb 22, 10:01:35 PM Watch help video Solve for all values of x : -6-(4x)/(x+2)=(8)/(x+2)
There is no solution for the equation -6-(4x)/(x+2)=(8)/(x+2).
To solve for all values of x in the equation -6-(4x)/(x+2)=(8)/(x+2), we need to use the following steps:
Step 1: Multiply both sides of the equation by (x+2) to eliminate the denominators. This gives us:
-6(x+2) - 4x = 8
Step 2: Simplify both sides of the equation by distributing and combining like terms. This gives us:
-6x - 12 - 4x = 8
-10x - 12 = 8
Step 3: Add 12 to both sides of the equation to isolate the variable on one side. This gives us:
-10x = 20
Step 4: Divide both sides of the equation by -10 to solve for x. This gives us:
x = -2
However, we need to check our solution to make sure it is not an extraneous solution. If we plug x = -2 back into the original equation, we get:
-6 - (4(-2))/(-2+2) = (8)/(-2+2)
-6 - (-8)/0 = (8)/0
Since we cannot divide by zero, our solution of x = -2 is an extraneous solution and there are no valid solutions to this equation. Therefore, the answer is no solution.
To know more about extraneous solution. click on below link:
https://brainly.com/question/28362830#
#SPJ11
Find the missing number to create a perfect-square binomial
___ y2-36y+81
Answer:
To create a perfect-square binomial of the form (y - k)^2, we need to find the value of k such that:
the first term of the binomial is y^2 (which is already the case)
the second term of the binomial is -2ky (which corresponds to -36y in the given expression)
the third term of the binomial is k^2 (which corresponds to 81 in the given expression)
To find k, we can use the formula:
k = (1/2)*(-b/a)
where a is the coefficient of y^2, b is the coefficient of y, and we are looking for the value of k that makes the expression a perfect square.
In this case, a = 1 and b = -36, so:
k = (1/2)(-b/a) = (1/2)(-(-36)/1) = 18
Therefore, the missing number to create a perfect-square binomial is 18:
(y - 18)^2 = y^2 - 36y + 324
heeeellllllpppppp i havent done decimals and shaded parts in a whileeeee
Answer:
0.40 or 40% is shaded
Step-by-step explanation:
There are 40 shaded out of the 100 squares. Therefor, .40 is the answer
2 Three different forces act on an object. They are: -- F1 = F2 = F3 = < -2, -3 > Find the net force Fnet on the object (the sum of the forces) Fnet = Find what fourth force, FA would need to be add
So the fourth force FA that would need to be added to make the net force zero is < 6, 9 >.
The net force on an object is the sum of all the forces acting on it. In this case, there are three different forces acting on the object: F1, F2, and F3. Each of these forces has a magnitude of < -2, -3 >. To find the net force Fnet, we simply add up all the forces:
Fnet = F1 + F2 + F3
Fnet = < -2, -3 > + < -2, -3 > + < -2, -3 >
Fnet = < -6, -9 >
To find the fourth force FA that would need to be added to make the net force zero, we simply need to find a force that is equal and opposite to Fnet. That is:
FA = -Fnet
FA = -< -6, -9 >
FA = < 6, 9 >
So the fourth force FA that would need to be added to make the net force zero is < 6, 9 >.
Learn more about net force
brainly.com/question/29261584
#SPJ11
The polynomial p(x) had the following roots: 5,-6,3-2i. Write the polynomial in factored form.
The polynomial in factored form is: (x-5)(x+6)(x-(3-2i))(x-(3+2i))
Since complex roots always come in conjugate pairs, we know that if 3-2i is a root, then 3+2i must also be a root. Therefore, we can write the polynomial in factored form by multiplying together the factors (x-5), (x+6), (x-(3-2i)), and (x-(3+2i)).
Alternatively, we can write the polynomial in factored form using the formula for a polynomial with complex roots:
p(x) = (x-r1)(x-r2)(x-r3)(x-r4)
where r1, r2, r3, and r4 are the roots of the polynomial. In this case, r1 = 5, r2 = -6, r3 = 3-2i, and r4 = 3+2i. Substituting these values into the formula gives us:
p(x) = (x-5)(x+6)(x-(3-2i))(x-(3+2i))
Therefore, the polynomial in factored form is written in the following form: (x-5)(x+6)(x-(3-2i))(x-(3+2i)).
To know more about Polynomial:
https://brainly.com/question/11536910
#SPJ11
solve 2t+3=12
and working please xx
Someone please answer and explain a & b. Image attached, thanks.
Jada has earned a total of 400 points so far.
141 + 87 + 81 + 91 = 400
There are a total of 450 points possible so far.
150 + 100 + 100 + 100 = 450
Jada has 400/450 or about 88.89% of the possible points, so no, she does not have 90%.
Adding in a 100-point test, the total number of points would become 550 and 90% of 550 is 495 points.
0.90 x 550 = 495
To finish the class with an A, Jada needs to have 495 points. She currently has 400 points. This means she needs a 95 on the final to finish the class with an A.
a phone tree is planned to get the word out quickly as possible about a schedule change at school suppose Step 1 it the lead person calling 5 people. Step 2 is those 5 people each calling 5 new people. This process continues until all the people on the phone tree have been called answers
By answering the above question, we may state that Once everyone on unitary method the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.
What is unitary method ?The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply expressed, the unit technique is used to extract a single unit value from a multiple that is provided.
First, the coordinator phones five persons to let them know that the school's schedule is changing.
Step 2: Those 5 people then each phone 5 more people, resulting in a total of 25 people receiving the news.
Step 3: The 25 call 5 additional individuals each, reaching a total of 125 people.
Step 4: The 125 call 5 additional individuals apiece, reaching a grand total of 625 persons.
Step 5: A total of 3,125 individuals have been told after the 625 phone 5 further persons each.
Once everyone on the phone tree has been contacted and advised of the schedule change, the procedure may be repeated.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1