Answers
Quadratic Standard Form:
ax²+bx+c=0
Replace = sign with <:
ax²+bx+c<0
So, we want to get 0 on the right side of the inequality to be in standard form.
To do this, we’ll add 18 to both sides:
x²-9x+18<0
This cancels out the -18 on the right, making it 0 because -18+18=0, and of course to keep the equation equal, we must add 18 to the left side as well.
Now, let’s understand the inequality. In standard form, a quadratic is equal to 0 to find the zeros. This is so that we can find what x-values will produce an output (y-value) of 0, as a y-value of 0 means no vertical change. It shows what x-values intercept the x-axis, which are the zeros (or roots) of the quadratic. Therefore, this inequality means: what x-values are less than 0, or go below the x-axis. To find this, we will factor the quadratic to see what x-values produce y-values less than 0.
Factor:
We know that -3-6=-9 and -3•-6=18
(x-3)(x-6)<0
So, the zeros of the function are x=3, 6. However, for x-values 3 and 6, the output is 0 since these values are x-intercepts. The inequality states less than 0, so we need look at x-values that produce a negative output.
So, if x=3, 6, then x>3 and x<6. Let’s look at the graph:
Related Questions
2. Write a factored form function, f(x) for a cubic function that has zeros (- 7, 0) and (3, 0)
Answers
The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).
How to derive a cubic equation in factor form
Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:
y = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Real zeros.Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)
f(x) = (x + 7) · (x - 3) · (x - r)
Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.
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Ron killed 8 times as many spiders as Harry,H (Write an expression to represent the following situations)
Answers
Answer:
Ron killed 8 times as many spiders as Harry: R = 8 * H
Step-by-step explanation:
This expression represents the situation in which Ron killed 8 times as many spiders as Harry.
Kaj and her children went into a grocery store and she bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought 2 more apples than bananas. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Kaj bought.
Answers
Kaj bought 3 bananas and 5 apples.
Finding the numbers of apples and bananas using substitution method.To determine the number of apples and bananas that Kaj bought, we can set up a system of equations.We know that the total amount spent on apples and bananas is $8.We know that each apple costs $1 and each banana costs $0.50.We know that Kaj bought 2 more apples than bananas.From these three pieces of information, we can set up the following two equations:
x + y = 8 (The total number of apples and bananas is 8)x + 0.5y = 8 (The total amount spent is $8)x = y + 2 (Kaj bought 2 more apples than bananas)We can substitute the third equation into the first equation and get:
y+2 + y = 8
So we know that y = 3
Now we can substitute this value into the second equation and get:
x + 0.5(3) = 8
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
And also we can substitute y = 3 into the third equation and get:
x = y + 2
So we know that x = 5
So Kaj bought 3 bananas and 5 apples.
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When 32 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution
Answers
Step-by-step explanation:
x² - 32 = 4x
x² - 4x - 32 = 0
with a little bit experience we see immediately that this is
(x - 8)(x + 4) = 0
the positive x for this to be true is x = 8.
formally, the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =
= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =
= (4 ± 12)/2 = 2 ± 6
x1 = 2 + 6 = 8
x2 = 2 - 6 = -4
we were right at the beginning.
the positive solution is x = 8.
Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7. What is the probability of her not winning? Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
Answers
The probability that Sabreena is going to lose is given as 0.5833
How to solve for the probabilityProbability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.
A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.
If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7
In this case, the odds of Sabreena winning are 5:7,
so the probability of winning is 5/(5+7)
the probability of not winning is 1 - 5/12
The probability of not winning is approximately 0.5833
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I need help solving for x
Answers
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
What Does Solve for x Mean?Let's begin with a straightforward equation: x + 2 = 7.
How do you obtain X on your own?
Take away two from both sides.
⇒ x + 2 - 2 = 7 - 2\s⇒ x = 5
Check the solution, x = 5, by reentering it into the equation. We get 5 + 2= 7.
R.H.S. L.H.S.
Utilizing triangle properties or the Pythagorean theorem, we can get a solution for the unknown side or angle of a triangle.
With the aid of an example, let's clarify how to solve for x in a triangle.
Two of ABC's legs, which measure 7 units and 24 units respectively, are right-angled at B. Look for the hypotenuse X.
By using the Pythagorean theorem to ABC,
We obtain AC2 = AB2 + BC2, where x2 = 72 + 242, 49 + 576, and 625 where x2 = 625.
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Which expression is equivalent to 12x2+x−20
Answers
If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered. 12x2 + x + 20 is the same as the given expression.
What other expression is the same as 3 5?6/10, 9/15, 12/20, etc. are fractions that are identical to 3/5. The value of equivalent fractions remains unchanged when lowered. Explanation: The numerator and denominator of equivalent fractions can be written by multiplying or dividing them both by the same value.
The given quadratic expression 12x^2+x-20
now, 12x^2 + 16x - 15x - 20
4x (3x+4) - 5(3x+4)
(4x-5) (3x+4)
the root of the equation is (4x-5) (3x+4)
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Simplify: [tex]\frac{10^4}{10^6}[/tex]
Answers
Answer:
1/100, or 0.01, or 10^-2
Step-by-step explanation:
Simplify to get 1/10^2
and evaluate to get 1/100 or some the alternative forms (see above)
y = 2x + 3
y = 2x + 1
Answers
Answer:
This is how you graph it
Step-by-step explanation:
As seen in the equations above, this equation can fit into the equation y=mx+b. M = slope, where is how we will be able to plot the points. Since the slope for both is two, we would go up 2 then right 1, from the y intercept. Which is the point we will be starting at. Plot two points directly on the y-axis at (0,3) and (0,1). Then go back to the slope and go up 2 and right 1. I hope I helped!
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Use the image below for Part A, Part B, and Part C.
Two triangles: GHI and JKL
Both have one similar angle but different side lengths
Part A: Sharon says the triangles above are similar using the AA Postulate. Is she correct?
Part B: Explain the answer from Part A.
Part C: If HI=7, find KL. Show your work.
Please Help!
Answers
Answer:
see explanation
Step-by-step explanation:
A
for the triangles to be similar by the AA postulate then 2 angles in both triangles must be congruent.
In this case we are only given 1 pair of congruent angles.
Thus not able to say similar by AA postulate, therefore Sharon is incorrect in her assumption.
B
the sides are of different lengths but the ratios of corresponding sides are equal, that is
[tex]\frac{JK}{GH}[/tex] = [tex]\frac{8}{4}[/tex] = 2 and [tex]\frac{JL}{GI}[/tex] = [tex]\frac{10}{5}[/tex] = 2
If the ratios of 2 pairs of corresponding sides of 2 triangles are equal and the included angles are congruent , then the triangles are similar, so
Δ GHI and Δ JKL are similar by the SAS postulate
C
the ratios of corresponding sides are equal , then
[tex]\frac{KL}{HI}[/tex] = [tex]\frac{JL}{GI}[/tex]
[tex]\frac{KL}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
KL = 14
Find the measurement indicated in each parallelogram.
Answers
Therefore , the solution of the given problem of parallelogram comes out to be option D 80 degrees.
Define parallelogram.A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Here,
Given : The parallelogram has M angle =100 degree
And to Find :L angle
In a parallelogram sum of the adjacent angle is 180°, So
So ,
Using this parallelogram property ,
we find :
=>100 + L =180
=> L = 80
Thus,
We get the L value using parallelogram properties.
Therefore , the solution of the given problem of parallelogram comes out to be option D 80 degrees.
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A recipe calls for 2 2/3 cups of flour to make two regular batches of cookies. Shiloh needs to make multiple batches of cookies. Represent this situation with an equation. What is the constant of proportionality? How can you identify it in an equation? How can you use an equation to determine if a relationship is proportional?
Answers
This situation can be represented with an equation as y = mx + b. The constant of proportionality (m) is a number that represents how much flour is needed for each additional batch of cookies. If the equation is in the form y = mx + b, then the relationship is proportional.
Shiloh needs to make multiple batches of cookies from a recipe that calls for 2 2/3 cups of flour to make two regular batches. To represent this situation in an equation, the equation is y = mx + b, where y is the amount of flour needed for the number of batches (x) Shiloh is making, m is the constant of proportionality, and b is the initial amount of flour needed (2 2/3 cups).
The constant of proportionality (m) in the situation above is the measure of how much flour is needed for each additional batch of cookies. For example, if the constant of proportionality is 0.75, that means Shiloh would need to add 0.75 cups of flour for each additional batch of cookies.
Therefore, if Shiloh is making three batches of cookies, the equation would be y = 0.75x + 2 2/3, and the total amount of flour needed would be 4 1/8 cups (2 2/3 + 0.75 + 0.75).
By using an equation to represent this situation, it is easy to determine if a relationship is proportional.
If the equation is in the form y = mx + b, then the relationship is proportional.
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Select the equation in standard form for the line that passes through (-9, 8) and (1, -12).
A) x + 2y = -20
B) 2x + y = -13
C) 2x+y = 7
D) 2x+y = -10
E) x + 2y = 20
Answers
Answer: D
Step-by-step explanation:
Since we are given 2 points, we can use that to find slope, convert to slope-intercept form, and then manipulate it to be standard form. Standard form is ax+by=c.
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-12-8}{1-(-9)} =\frac{-20}{10} =-2[/tex]
With m=-2, we can plug it into slope-intercept form to find the y-intercept.
[tex]y=-2x+b[/tex] [plug in point]
[tex]8=-2(-9)+b[/tex] [multiply]
[tex]8=18+b[/tex] [subtract both sides by 18]
[tex]b=-10[/tex]
With m and b, we can plug in the equation.
[tex]y=-2x-10[/tex] [add both sides by 2x]
[tex]2x+y=-10[/tex]
This gives D as the answer.
Hassan plans to repaint some classroom bookcases. He has 1010 gallons of paint. All of the bookcases are the same size and each requires \tfrac{7}{8}
8
7
gallon of paint. What is the maximum number of complete bookcases he can paint?
Answers
Hassan can paint maximum 11 bookcases with 10 gallons of paint.
What are Fractions?A fraction represents a numerical value, which defines the parts of a whole.
Generally, the fraction can be a portion of any quantity out of the whole thing and the whole can be any specific things or value.
The basics of fractions explain the top and bottom numbers of a fraction.
Suppose a number has to be divided into four parts, then it is represented as x/4. So the fraction here, x/4, defines 1/4th of the number x. Hence, 1/4 is the fraction here.
Given,
Hassan has 10 gallons of paints.
1 bookcase requires 7/8 gallons of paint
Let Hassan paints x bookcases.
According to the question
7/8x = 10
7x = 80
x = 80/7
x = 11.43
But no. of bookcases should be in whole.
Number of bookcases painted with 10 gallons of paint = 11.
Hence, Maximum 11 bookcases can be painted by Hassan with 10 gallons of paint
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The temperature was recorded at midnight for 5 consecutive days. The
recorded temperatures are: -2°, 4°, 5°, -6°, and 9°. What is the average
temperature?
Answers
How many possible real solutions are there?
Answers
The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
A linear equation (degree 1) has one real solution.
A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.
A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.
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How do you find the value of 3 7?
Answers
Step-by-step explanation:7/3 and if it goes in a inf loop it's a repeating
The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYY
Answers
The area of the floor in the scale drawing is 60 inches²
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangular floor.
Length = 24 feet
Width = 40 feet
Scale rectangular floor.
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scale rectangular floor.
= Length x Width
= 6 x 10
= 60 icnhes²
Thus.,
The area of the floor is 60 inches².
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How do you solve the equation 5t 3 3t 5?
Answers
By solving the equation 5t - 3 = 3t - 5 we get the equation is true when t = -1. So the solution is t = -1.
To solve the equation 5t - 3 = 3t - 5, you can use algebraic manipulation to isolate the variable on one side of the equation.
The first step is to get all the terms with the variable on one side of the equation and all the constant terms on the other side.
5t - 3 = 3t - 5
adding 3 to both sides:
5t = 3t - 2
subtracting 3t from both sides:
2t = -2
then divide both sides by 2:
t = -1
So the solution is t = -1, meaning that when t = -1, the equation is true.
--The question is not clear, answering to the question below--
"How do you solve the equation 5t - 3 = 3t - 5?"
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The vertices of a convex pentagon are $(-1, -1), (-3, 4), (1, 7), (6, 5)$ and $(3, -1)$. What is the area of the pentagon
Answers
On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit
what is a pentagon?A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.
vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).
Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]
Area = 1/2| 60 |
Area of pentagon = 30 sq unit
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What is the solution to the system of equations below x y 7 and x 2y 11?
Answers
The solution to the system of equations is x = 3 and y = 4.
this question is related to system of equations ,
the equations are,
x + y = 7 .......[1]
x + 2y = 11
x= 11 - 2y
now, place the value of x in equation 1,
(11 - 2y) + y = 7
11 - 2y +y = 7
11 - y = 7
- y = 7 - 11
- y = - 4
y = 4
now to find the value of x, place the value of y in equation 1
x + 4 = 7
x = 7 - 4
x = 3.
so, the value of x and y is 3 and 4.
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A triangle has an angle that measures 126°. The other two angles are in a ratio of 11:16. What are the measures of those two angles?
Answers
Therefore, the measures of those two angles are 33° and 24°.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which means "corner," is the source of the English term "angle."
Define geometry.Geometry is a branch of mathematics that studies the sizes, shapes, positions, angles, and dimensions of things.
We know, the sum of the angles in a triangle is always 180 degrees.
126 + x + y = 180
x + y = 54
Given that the two angles are in a ratio of 11:16, the proportion:
x/y = 11/16
Solving for x and y, we get:
x = 11y/16
We substitute this equation into the equation x + y = 54 and we get:
11y/16 + y = 54
Solving for y we get y = 24. Then we can use the proportion to find x:
x = 11 * 24 / 16 = 33.
So the two angles are 33° and 24°.
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How much of a radioactive kind of barium will be left after 39 days if you start with 52,256 grams and the half-life is 13 days?
Answers
Answer:
Step-by-step explanation:
Answer:
6,532
Step-by-step explanation:
ixl
PLS HELP ASAP I DONT NNOW HOW TO DO THIS
Answers
Answer:
I think you do know how because where the point is now is correct!!
Denise dusted a square tabletop with an area of 36x^16y^4 units write an expression to represent one side length of the table top
Answers
The length of the side of the table top as calculated from the given data will be 6x⁴y².
To calculate the area of the table top we will have to square of the sides given .
area =(36x.16y^4 )²
side =√(36x.16y^4 )²
= 6x⁴y².
In mathematics the product of a number multiplied by itself is considered to be its square. Eg.) 6 multiplied by 6 gives 36 which is known as its square.
The given table is square in shape and hence its area will be given my multiplying its side with itself.
Area of a square = side x side.
To find its length we can simply find the square root of the number.
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6 m
5 m
3 m
Find the area of this figure. Round your
answer to the nearest hundredth.
Use 3.14 to approximate T.
A = [?] m2
Answers
The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.
given
Three shapes—a rectangle, a triangle, and a semicircle—make up the figure.
Triangle + rectangle + semicircle together make up the figure's surface area.
Triangle's area is equal to 1/2 * 3 * 5.
Triangle's surface area is 15/2.
Triangle's surface area is 7.5 m3.
Rectangle area equals length times width
Rectangle's area is equal to 6 x 5.
30 m2 is the rectangle's area.
Semicircle area equals πr²/2
Semicircle's area is equal to π(3)²/2
Semicircle's area is equal to 3.14(9)/2.
Semicircle's area is equal to 3.14 x 4.5.
Semicircle's surface area is 14.13 m2.
Area: 30 + 14.13 + 7.5
The area occupied by the semicircle, rectangle, and right-angled triangle in the figure is 51.63 m3.
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What is the difference of the two polynomials 9x 2 8x 2x 2 3x?
Answers
The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.
What is polynomial?A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Here,
The difference between the two polynomials (9x²+8x)-(2x²+3x) is 7x²+5x.
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OrScruffy Pals Pet Boxes sends pet supplies in the mail each month. Irma prepaid a 4-month subscription for her cats. She used a one-time coupon and received $8 off the total cost. Irma paid $64 in all. Which equation can you use to find m, the regular cost per month?
Answers
We employ the following equation to get the normal monthly cost:
4m - 8 = 64
Regular monthly expenses amount to $18.
Irma paid for her cats' subscription in advance for a 4-month period.
She saved $8 overall when she utilized a one-time discount.
Irma totaled $64 in payment.
We must identify the equation that can be utilized to calculate m, the average monthly cost.
Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.
When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.
Irma paid a total of $64 according to the problem, thus we can create the following equation:
4m - $8 = $64
We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.
4m = $64 + $8
4m = $72
Finally, divide both sides by 4 to solve for m:
m = $72 / 4
m = $18
So, the regular cost per month, m, is $18.
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Which expression is not equivalent to logp 36? 1. 6 log 2 2. log 9+ Iog, 4 O 3 2 logb 6 4. log 72 logp 2
Answers
log 30+ log 6 is not equivalent to log 36
What is equivalent expressions?Equivalent expressions are expressions that perform the same function not with standing their appearance. If two algebraic expressions are equivalent, they have the same value when the same value(s) for the variable are used (s).
The original phrase is as follows
Log 36
Following that, we write the alternatives (a) log 2+ log 18
Apply the logarithmic rule log 2+ log 18 log (218)
Log 2 plus log 18 log (36)
Remove the bracket
Log 2 plus log 18 log36
(a) Log 2+ Log 18 is the same as log 36.
(b) Log 30 plus log 6
Use the logarithms’ law. 30 logs or more 6 logs (30 x 6)
Log 30 plus log 6 Equals log (180)
Remove the bracket
Log 30-plus log 6-log180
Hence,
(c) Log 30+log 6 does not equal log 36.
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L) simplify
sin²x ( cot²x + 1 )
Answers
Answer: 1.
Step-by-step explanation:
[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]