Answer:
Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit or formulating the speed of an object. Quadratic equations refer to equations with at least one squared variable, with the most standard form being ax² + bx + c = 0.
Here is an example:
Antoine stands on a balcony and throws a ball to his dog, who is at ground level.
The ball's height (in meters above the ground), xxx seconds after Antoine threw it, is modeled by:
h(x)=-2x^2+4x+16h(x)=−2x
2
+4x+16h, left parenthesis, x, right parenthesis, equals, minus, 2, x, squared, plus, 4, x, plus, 16
What is the height of the ball at the time it is thrown?
____meters
here is another example:
2x2 + 5x + 3 = 0 = In this one a=2, b=5 and c=3
Hope that was helpful.Thank you!!!
Answer:
see below
Step-by-step explanation:
Often, the simplest way to solve "ax2 + bx + c = 0" for the value of x is to factor the quadratic, set each factor equal to zero, and then solve each factor. But sometimes the quadratic is too messy, or it doesn't factor at all, or you just don't feel like factoring. While factoring may not always be successful, the Quadratic Formula can always find the solution.
The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.
The Quadratic Formula is derived from the process of completing the square, and is formally stated as:
The Quadratic Formula: For ax2 + bx + c = 0, the values of x which are the solutions of the equation are given by:
-b ± [tex]\sqrt{b^2 - 4ac}[/tex]
x = ----------------------------------
2a
A sphere has a radius of 3 ft. What is the volume of the sphere? Give the exact value in terms of Pi.
Answer: 36π
Step-by-step explanation:
equation
V= 4/3(pi)r^3
Which of these polygons is not formed by the cross-section created when a plane intersects a cube? Select all that are possible.
square
circle
pentagon
octagon
triangle
rectangle
Answer:
Circle
Octagon
Step-by-step explanation:
There are no curves in a cube to make a circular cross section, and there aren't enough edges to make an octagon (just visualize)
Answer:
A circle is not possible. Neither is a square or a rectangle.
Step-by-step explanation:
Write an equivalent
expression for
88 + 16x + 8
Answer:
16x + 96
Step-by-step explanation:
You can add 88 + 8 for and get the same answer
Answer: 16x+8+88
Step-by-step explanation:
All you need to do is move around the numbers and then you get the answer
At a certain time of day, the angle of elevation of the sun is 40°. To the nearest foot,find the height of a tree whose shadow is 35 feet long.
Which value is equivalent to 2 x 3 + 4 -
6^2?
A. -26
B. -22
C. -2
D. 10
The floor function maps any number to the greatest integer that is _[blank]_ the number.
Which phrase correctly fills in the blank of the previous statement?
A.) greater than
B.) greater than or equal to
C.) less than or equal to
D.) less than
Answer:
C. Less than or equal to
Step-by-step explanation:
The floor function is a function used to return an integer value that is great than the input number.
More often than not, the input number is a real number.
Take for instance.
Floor(3.2).
Going by the explanation above, the result of this will be 3
How about floor(-3.2)
The result of this will be -4.
This is so because -4 is less than or equal to -3.2.
The floor function maps any number to the greatest integer that is C.) less than or equal to the number.
The floor function maps any number to the greatest integer that is less than or equal to the number. This means that for any real number \( x \), the floor function, denoted as [tex]\( \lfloor x \rfloor \),[/tex] will produce the largest integer that does not exceed \( x \). For example, \( \lfloor 3.7 \rfloor = 3 \) and \( \lfloor -2.3 \rfloor = -3 \).
The floor function is widely used in mathematics and computer science for rounding down numbers to the nearest integer. It is especially useful in discrete mathematics, algorithms, and number theory. When working with the floor function, it is essential to understand that it always rounds down towards negative infinity, not necessarily towards zero. Thus, for any real number \( x \), \( \lfloor x \rfloor \leq x \).
Therefore, the correct phrase to complete the statement about the floor function is:
C.) less than or equal to.
Solve 2x² -9x-5=0 by factoring. what is the
Solution?
Answer:
0
Step-by-step explanation:
Write 6,020,300 in expanded form.
Answer:
6,000,000 + 20,000 + 300
Step-by-step explanation:
Point A is at (-2,-7) and point B is at (7,4).
What is the midpoint of line segment AB?
The coordinates of the midpoint would be (5/2, -3/2) of line segment AB.
What is Midpoint?A midpoint is defined as in the middle of the line connecting two points a position known as a midpoint. A location in the middle of a line connecting the two points that are equally far from both points is the midpoint.
Let two points A (x₁, y₁) and B (x₂, y₂), the midpoint between A and B is given by,
M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Coordinates of A are (-2,-7),
Coordinates of B are (7, 4),
M is the midpoint of AB which is given in the question
So the coordinates of M as:
⇒ M(x, y) = (x₁ + x₂)/2, (y₁ + y₂)/2
Substitute the values, and we get
⇒ M = ((-2 + 7)/2, ( -7 + 4)/2)
⇒ M = ((5)/2, ( -3)/2)
⇒ M = (5/2, -3/2)
Therefore, the coordinates of the midpoint would be (5/2, -3/2) of line segment AB.
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Connie collected 50 seashells during her 5-day vacation. Each day she collected 3 more than the previous day. How many seashells did she find each day? PLEASE HELP!
Answer:
The number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively
Step-by-step explanation:
This is a question that deals with consecutive numbers.
Let x represent the number of seashells collected on her first day.
Given that she collected 3 more each day, then
On day 2, she collected x + 3
On day 3, she collected x + 6
On day 4, she collected x + 9
On day 5, she collected x + 12
Adding up the above will give the number of sea shells collected on day 1;
i.e.
x + x + 3 + x + 6 + x + 9 + x + 12 = 50
Collect like terms
x + x + x + x + x + 3 + 6 + 9 + 12 = 50
5x + 30 = 50
5x = 50 - 30
5x = 20
Multiply ⅕ to both sides
⅕ * 5x = ⅕ * 20
x = 4.
This mean that she found 4 seashells on day 1;
Recall that day 2 = x + 3
So, day 2 = 4 + 3 = 7 seashells
day 3 = x + 6
day 3 = 4 + 6 = 10 seashells
day 4 = x + 9
day 4 = 4 + 9 = 13 seashells
day 5 = x + 12
day 5 = 4 + 13 = 16 seashells
Hence, the number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively
Mrs.Brown gives two tests to her class. 30% of the class passed both tests and 45% of the class passed the first test. What percent passed the second test given that they passed the first test?
Answer:
15%
30 percent passed BOTH tests.....Only 15% passed ONLY first test
30/(30+15) = 67% of those who passed the first test ALSO passed the second test.
-10° i need help pleaseeee
Which number is the additive inverse of -5?
Answer:
It would be 5
Step-by-step explanation:
SO the additive inverse would basically just be the opposite of the number, for example lets say you had 12, the additive inverse would be -12. You're just changing the sign of the number! From what i know i believe that's it. Have a nice day! :D
Multiply.
Your answer should be a monomial in standard form.
(Y^8)(-2y²) =
[tex]( {y}^{8} )( - 2 {y}^{2} ) = - 2 {y}^{10} [/tex]
To multiply the monomials (Y⁸)(-2y²), add the exponents and multiply the coefficients resulting in -2y¹⁰.
To multiply the given monomials (Y⁸)(-2y²), we use the laws of exponents which state that when multiplying like bases, we add the exponents. The coefficient -2 multiplies by 1 (the implied coefficient of Y⁸) to remain -2. The new exponent for 'y' is the sum of 8 and 2, which is 10. So, the product in standard form is -2y¹⁰.
Step by step solution:
Identify like bases, which in this case is 'y'.Add the exponents of 'y' (8 from Y^8 and 2 from y²) to get a new exponent of 10.Multiply the coefficients (1 and -2) to get -2.Write the final answer combining the new coefficient and the new exponent of 'y': -2y¹⁰.Drew’s dog weighs 24 lb 5 oz. How many ounces does drew’s dog weigh?
Answer:
Step-by-step explanation:
It weighs 389 pounds so the answer would be C.
Help me please
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Answer:
2
Step-by-step explanation:
The Fundamental theorem of algebra states that a polynomial of degree n has n roots. These can be real or complex.
A quadratic is of degree 2 and has 2 roots.
HELP PLEASE WILL MARK BRAINIST
Answer:
i did the math and it should be B. 7 hours
Step-by-step explanation:
18/x=-2
what number does x represent
Answer:
9
Step-by-step explanation:
18/x = 2
or, 18 = 2x
or, 18/2 = x
or, 9 = x
ans ; x = 9
Which equation BEST represents the line of best fit for the scatterplot?
A) y = 3x
B) y = x - 2
C) y = x - 3
D) y = x + 3
Which point on the coordinate plane is located at (4,0)?
A) point A
B) point B
C) point C
D) point D
Answer:
point B
Step-by-step explanation:
The coordinates (4,0) is has the numbers 4 and 0.
4 is positive and can be represented as moving right on the origin. Since, there is no rise it stays.
i really need help! can someone help me
Answer:
M + $13.72 = $58.22
Step-by-step explanation:
Manny and Sam combined (+) have a total (=) of $58.22
M + S = $58.22
M + $13.72 = $58.22
Answer:
m + $13.72 = $58.22
Step-by-step explanation:
Together they have $58.22.
We know one of them has $13.72, so if we add that to (m) we should get $58.22.
A town with a population of approximately 20,530 people is planning to build a new park. The town government is trying to find out what entertainment options citizens would prefer the park to include and plans to survey people running the trail in the existing park over a period of a month.
Answer:
Step-by-step explanation:
Write the following equation in slope-intercept form: 4x – 5y = 15.
Answer:
y = (4/5)x - 3
Step-by-step explanation:
slope intercept form: y = mx + b
Note the equal sign, what you do to one side, you do to the other. First, subtract 4x from both sides:
4x - 5y = 15
4x (-4x) - 5y = 15 (-4x)
-5y = -4x + 15
Next, divide -5 from both sides:
(-5y)/-5 = (-4x + 15)/-5
y = (-4x + 15)/-5
Simplify Divide -5 from all terms within the parenthesis:
y = (4/5)x - 3
y = (4/5)x - 3 is your answer.
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What is the simplified expression for the expression below
Bill is playing a game of chance with the following payout. 30% of the time you will lose 20 dollars, 20% of the time you will lose 40 dollars. 10% of the time you will win 50 dollars, 40% of the time you will win 5 dollars. Find the expected value of the event and explain if Bill should play this game based on the mathematical expectation.
please helpppop asappppp and show work so I understand please
Anybody know this??? please help
Answer:
The expected value of playing the game is -$7.
Bill should not play this game.
Step-by-step explanation:
The probability distribution of gain and loss is as follows:
X P (X)
-$20 0.30
-$40 0.20
$50 0.10
$5 0.40
Total 1.00
The expected value of a probability distribution is given by:
[tex]E(X)=\sum {X\times P(X)}[/tex]
Compute the expected value of playing the game of chance as follows:
[tex]E(X)=\sum {X\times P(X)}[/tex]
[tex]=(-\$20\times 0.30)+(-\$40\times 0.20)+(\$50\times 0.10)+($5\times 0.40)\\\\=-\$6-\$8+\$5+\$2\\\\=-\$7[/tex]
The expected value of playing the game is -$7.
The expected value of the game suggests that Bill will incur a loss of $7 if he plays.
So, it is safe not to play the game.
On a coordinate plane, parallelogram A B C D is shown. Point A is at (negative 3, negative 1), point B is at (7, 9), point C is at (8, negative 1), and point D is at (negative 2, negative 11). Create a rectangle around the parallelogram. The dimensions of this rectangle are ____(1). Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is _____(2) square units. Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is ______(3) square units.
Answer: HOPE THIS HELPSS!!! please mark me brainliestt
11 by 20
110
110
Answer:
just wanted to say hi
Step-by-step explanation:
Plz give 5 star
Please help!! :) Cant solve it on paper currently since its late and just doing it online.
Answer:
14.4 in
Step-by-step explanation:
Using the formula of the Pythagorean theorem, a² + b² = c², we can find the length of the missing side.
a = 8
b = 12
c = ?
8² + 12² = 208
To get your answer, you must take the square root of 208.
√208 = 14.4222051
Which mathematical symbol would best fill in the blank to compare the two real numbers? (4 points) square root of 7 blank 14 over 5 Group of answer choices < > = ≈
Answer is <
Step-by-step explanation:
To compare the square root of 7 and 14 over 5, we find their approximate values. Since 2.65 (root 7) is less than 2.8 (14/5), the correct mathematical symbol to use is <.
Explanation:The question asks us to compare two real numbers: the square root of 7 and 14 over 5. First, we need to estimate these numbers. The square root of 7 is approximately 2.65. 14 divided by 5 equals 2.8. Therefore, we can say that 2.65 is less than 2.8. As such, the mathematical symbol that should be used is < which means 'less than'.
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Number eight, graph each question
Answer:
(1,3)
Step-by-step explanation:
x would be counted as (1,1) therefore, moving 1 number to the right, and 1 number up.
- Electricity City increases the price of televisions by 25%. If a television now sells for
$425, what was the original price?
Answer:
340
Step-by-step explanation:
Let x = original price
We increase by 25%
x+x*25% = new price
Change to decimal form
x+.25x = new price
Factor out the x
x(1+.25) = new price
x(1.25) = new price
x(1.25) = 425
Divide each side by 1.25
x = 425/1.25
x =340
The original price is 340