Write a quadratic equation with solutions -3 and 4/7.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
У = -16x^2 + 246x + 100
The rocket reaches a maximum height of 1045.6 feet.
How to find the maximum height of a parabola by quadratic formula
The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficients.x - Time, in seconds.y - Height, in feet.The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:
a · x² + b · x + (c - y) = 0
Discriminant
b² - 4 · a · (c - y) = 0
b² = 4 · a · (c - y)
b² / (4 · a) = c - y
y = c - b² / (4 · a)
If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:
y = 100 - 246² / [4 · (- 16)]
y = 1045.563 ft
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X^5 = -5 complex numbers using square roots
Poopy man is my husband uwu
anyways ur answer is 3^x
i’ll mark brainliest !!!!!
Answer: x =2
Step-by-step explanation: Since the two triangles have to shared sides then all sides must be equal so 9x-12=3x. -6x=-12 and x =2
Answer:
9x=12
so
x=12/9 = 4/3
and
(4-347-12)-(8+7-27)
PLEASE HELPPPP
Answer:
=4-347-12-8-7+27
=-343
*Mark me brainliest -_- *_*
Answer: (4-347-12)-(8+7-27)= -343
Determine the distance between the points (-2,3) and (5,-3):
The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
What is the distance?The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
So, we have the points:
(-2, 3) and (5, -3)
Distance formula: d=((x2 - x1)² + (y2 - y1)²)
Insert values and calculate as follows:
d=((5 - (-2))² + (-3 - 3)²)
d=((7)²+(-6)²)
d=√85
d=9.21
Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
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Which linear system could the graph represent?
Responses
A 4x + 4y = 4
x + y = 14x + 4y = 4 x + y = 1
B 2x − y = 4
x + 2y = −32x − y = 4 x + 2y = −3
C −x + y = 2
x + 2y = 2−x + y = 2 x + 2y = 2
D x + y = 2
2x + 2y = 8x + y = 2 2x + 2y = 8
Question 2
The system represented by the graph has how many solutions?
Responses
A 1
B 2
C 0
D infinitely many
The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8
So, Option D is correct.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)
Given that,
The graph of linear system
first line intersects the x & y axes at (2,0) & (0,2) respectively
Similarly, second line intersects the x & y axes at (4,0) & (0,4) respectively
By using two point form of the line we can write equation for both the lines,
x + y = 2 _____ (1)
x + y = 4 _____ (2)
by multiplying 2 in equation (2)
2x + 2y = 8
Hence, The linear system is x + y = 2 & 2x + 2y = 8
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16) Similar triangle 5
r
4
X
h
*) find y if h= 3
*) find X
find r
71
3
P
The values of the variables in the similar triangles are y = 2.25 units, x = 5 units and r = 3.75 units
How to find the variables in the similar triangles?Similar triangles are triangles that have the same shape, but possibly different size. Two triangles are similar if and only if their corresponding angles are congruent, that is, they have the same measure. When two triangles are similar, their corresponding side lengths are in proportion.
Since the triangles are similar. We write:
h/y = y/3
Since h = 3, we have:
3/4 = y/3
y = 9/4 = 2.25 units
x = √(4² + h²) (Pythagoras theorem)
x = √(4² + 3²) = 5 units
r = √(y² + 3²)
r = √(2.25² + 3²) = 3.75 units
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In a random sample of 8 customers, what is the probability that exactly 4 of them will use the Self-Checkout?
In the box below, give your answer correct to 3 significant figures. If you are correct, you will receive a CORRECT message here.
The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.
What is binomial probability?Binomial probability is the probability based on the binomial distribution.
The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.
The binomial distribution formula is:
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
P = binomial probability
x = number of times for a specific outcome within n trials
{ⁿ \ ₓ} = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
Random sample, n = 8
Specific outcome within n trials = 4
pˣ = 0.5⁴
= 0.0625
qⁿ = (1 - 0.5)⁸ ⁻ ⁴
= 0.5⁴
= 0.0625
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
= 8/4 x 0.0625 x 0.0625
= 2 x 0.0625 x 0.0625
= 0.0078125
= 0.008
Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.
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What are the answers to these
Step-by-step explanation:
Let’s use the equation: 3|2x-1|-8=-14
3(|2x−1|)−8=−14
Step 1: Add 8 to both sides.
3(|2x−1|)−8+8=−14+83(|2x−1|)=−6
Step 2: Divide both sides by 3.3. (|2x−1|)3=−63|2x−1|=−2
Step 3: Solve Absolute Value. |2x−1|=−2
No solutions. (Absolute value cannot be less than 0.)
Which point on the number line represents the difference 2.6 - 1.2?
The answer is 1.4
What is the number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
Given here:
2.6-1.2=1.4
Hence, The answer is 1.4
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1/2(x-5)=9 what is the value of x
Answer:
23
Step-by-step explanation:
1/2-2.5=9
1/2x=9+2.5
x=11.5/0.5
x=23
A diamond speculator used the line with equation
y = 5000x250 to estimate the price of diamond
rings.
5) What would the speculator predict fot he price of the
0.29-carat diamond ring?
6) What would the speculator predict fot he price of the
0.21 -carat diamond ring?
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
y = 5000x - 250
y = 5000 * 0.29 - 250
y = 1200
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
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Lucas is selling 4 pears for $5.45. How much will 5 pears
cost?
Answer:
6.8125
Step-by-step explanation:
HELPPPPPPPPPPPPPPP!!!!!
f(1) = -1
Step-by-step explanation:Quadratic equations form the shape of a parabola, which looks like a U-shape.
Graph
To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.
Equation
We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.
f(1) = 1² - 2f(1) = -1This also shows that f(1) = -1.
An arithmetic sequence is defined by fn = 7 + 8(n – 1). What is the value of f1
Answer:
f(11) = 87
Step-by-step explanation:
substitute n = 11 into f(n) , that is
f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87
Aunt Sue used 1/6 teaspoon of vanilla to make 2/12 containers of pudding. How much vanilla is in one container of pudding?
The amount of vanilla in one container of pudding is given as follows:
One teaspoon.
How to obtain the amount of vanilla?The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.
The rule of three is defined as follows:
1/6 teaspoon - 2/12 containers.
x teaspoon - 1 container.
The first line can be simplified as follows:
1/6 teaspoon - 1/6 containers.
(as 2/12 = 1/6).
Hence there is one teaspoon of vanilla in one container of pudding.
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Show the relationship between the number of miles and the number of hours in the ratio 24 to 2
The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
What is the ratio?
A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.
The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.
Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
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help I can't do math :')
1.20C + 3 >= 13.50
Where C is the number of chores Janie does.
On the left side of the inequality, 1.20C represents the amount of money Janie earns from doing chores, and 3 represents the amount of money she already has. The inequality states that the sum of the money she earns from doing chores and the money she already has must be greater than or equal to the cost of the CD (13.50).
This inequality can be simplified:
1.20C >= 10.50
C >= 8.75
Thus, Janie could do at least 8.75 chores to have enough money to buy the CD, since she can do fractions of chores.
Answer:
3 + 1.2 c > 13.50
Step-by-step explanation:
First of all, let's write an equation that gives us the income Janie gets for doing chores. As she earns 1.20 (I will omit the $ symbol for simplicity) for each chore c she makes we can write income depending on the amount of chores as:
income(c) = 1.2 c
If she does 1 chore she gets 1.2, if she does 4 chores she gets 4.8 and so on for any c (obviously c is positive as she can do negative chores).
So, her total money will be the sum of what she earns for chores and the money she already has: 3.
money (c) = 3 + 1.2 c
If she does 2 chores she has 3+2.4=5.4 and so on for any c.
Now we need her money to be greater or equal to 13.50 in order to buy the CD. The inequality is:
money (c) > 13.50
3 + 1.2 c > 13.50
We can go further and solve it. First lets subtract 3 in both sides:
12 c > 10.50
Now, divide both sides by 1.2:
c > 10.50 / 1.2
c > 8.75
So, she needs at least 8.75 chores to earn enough money to buy the CD. As she can do fractions of chores the answer is 8.75 chores. Is she couldn't do fractions she would need at least 9 chores.
A shopkeeper buys 1800 eggs st $1.20 per dozen. 5% of the eggs are rotten. Find the selling price of each egg if he wants to earn 33% profit on the cost price
$0.14 is the selling price of each egg.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that shopkeeper buys 1800 eggs $1.20 per dozen.
1 dozen = 12 eggs
So 1.20 ÷ 12 = $0.1 cost of one egg
Total cost (C) 1800×0.1 = $180
1800×0.95 = 1710 eggs to be sold
Profit % = 100×(SP - C)/C
33 = 100×(SP - 180/180
SP = $239.4
239.4 ÷ 1710 = $0.14 is the selling price of each egg.
Hence, $0.14 is the selling price of each egg.
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What is 249 rounded to the nearest 10?
Answer: 250
Step-by-step explanation:
249 is closer to 250 than 240
Answer:
Step-by-step explanation:
249 is rounded to closest to 250
Can you please help me i want to know the steps to solve this problem i dont want the answer so i can learn to do this on my own
Answer:
Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so
1+(6-8)=?
Mr. Coupe and his friend have 2,798
paddle balls to split among 40 hoppers.
How many will be in each hopper?
MULTIPLICATION
Estimate:
Solve:
DIVISION
Answer:
To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.
paddle balls ÷ hoppers = paddle balls per hopper
2798 ÷ 40 = 69.95
So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.
Step-by-step explanation:
I NEED HELP ASAP
8th grade Pre-algebra
Pre-algebra is a primary branch of algebra designed to prepare students for a standard high school algebraic course
In eighth grade, what is Pre-Algebra?Real number system, linear connections, functions, linear equations, systems of equations, geometric concepts such as transformations, Pythagorean Theorem and angle relationships, and scatter plots are all studied.You will learn about and investigate subjects such as integers, order of operations, algebraic expressions, one and two-step equations, proportions, percents, probability, geometry, and linear equations in Pre-Algebra.
Pre-algebra classes are intended to prepare pupils for a typical algebraic curriculum in high school. Integers, fractions, square roots, step equations, linear equations, and decimals are introduced to students. They will also learn how to use variables to solve basic problems.
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What is the measure of each angle inside the figure (the value of x)?
(Hint-This equals 360° divided by the number of sides of the figure.)
Answer:
60
Step-by-step explanation:
360 degrees divided by 6 sides equal 60 degrees
Represent Multiplication of
Whole Numbers by Fractions
raw a visual model to find the product.
2x
ME Critique Reasoning Barbara picked 36 apples. She
needs to put of the apples in a basket. Barbara says she
will put 12 apples in the basket. Is Barbara correct? HELP MEE
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
what is fraction ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
given
she is correct as Barbara picked 36 apples
in one time she put 12 apples in the basket
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
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What is Lateral surface area?
Answer:
The lateral surface of an object is all of the sides of the object, excluding its base and top (when they exist). The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.
1. a. Provide two independent events that you know the probability of.
b. Explain how you know these events are independent.
c. Find the probability that they both occur.
2. a. Provide two dependent events.
b. Explain how you know these events are dependent.
c. Explain why these dependent events might require a different method for calculating the probability of both events occurring.
Example of dependent events and independent events and their probabilities are as given below.
How to provide two independent events with known probability?1. a. Two independent events that I know the probability of are:
Rolling a fair die and getting a 4 (probability of 1/6)
Flipping a fair coin and getting heads (probability of 1/2)
b. I know these events are independent because the outcome of one event does not affect the outcome of the other event. The outcome of rolling a die does not affect the outcome of flipping a coin, and vice versa.
c. The probability of both events occurring is (1/6) × (1/2) = 1/12
2a. Two dependent events:
i. Drawing a red card from a deck of cards and then drawing another card (without replacement)
ii. Drawing a red ace and then drawing another red card (without replacement)
b. I know these events are dependent because the outcome of the first event affects the outcome of the second event. The probability of the second event depends on the outcome of the first event.
c. These dependent events might require a different method for calculating the probability of both events occurring, such as conditional probability.
The probability of both events occurring would be P(A and B) = P(A) × P(B|A)
where P(A) is the probability of the first event and P(B|A) is the probability of the second event given that the first event has occurred.
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solve the given differential equation by undetermined coefficients. y'' + 2y = −18x2e2x
The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).
The given differential equation is y'' + 2y = −18x^2e^(2x)
To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.
The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)
Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form
yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).
Substituting this into the differential equation, we get
y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)
Equating the coefficients of the like terms, we get:
6A = 0, 2B = −18, and 2C = 0
Solving for A, B and C, we get A = 0, B = −9 and C = 0
Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)
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A teacher gave her students two tests. If 45% of the students passed both tests and 60% passed the first test. What is the probability that a student who passed the first test also passed the second?
Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.
The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).
We can use the information provided to calculate this probability:
Probability of passing both tests = 0.45 (45%)
Probability of passing the first test = 0.60 (60%)
Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75
So the probability that a student who passed the first test also passed the second is 0.75 or 75%.
It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.
Step-by-step explanation: