The coefficient of x² in (3x² – 5)( 4 +4x²) is -8.
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6.
First, let's multiply the terms in the given expression by opening the brackets.
⇒ (3x² – 5)( 4 +4x²)
Now, further multiplying we would get,
⇒ 3x²(4 + 4x²) -5(4 + 4x²)
⇒ 12x² +12x⁴-20-20x²
⇒ 12x⁴ -8x²-20
As we can see that the term that is in multiplication with x² is -8. Similarly, the term that is coefficient of x⁴ is +12.
Hence, the coefficient of x² in the equation is -8.
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it possible to create an equation for a circle given exactly two points. describe exactly how one would do this. provide an example if necessary.
It is impossible to create an equation for a circle given exactly two points.
Let's consider the two basic equations of circle, i.e, the standard equation and general equation.
Now, Standard equation of circle with center (h, k) and radius r is represented as
(x−h)² +(y−k)² =r²
Note here we need values of three unknowns, h, k, r to get equation of a certain circle.
The other general equation of circle is of the form
x² + y² + 2gx + 2fy + c = 0
Again, values of three unknowns (g, f and c) are necessary for obtaining equation of a certain circle. So in both cases, values of three unknowns are required to have an equation of a distinct circle. In order to calculate, the values of these three unknowns, we must first require three conditions that would be produced by three equations. Solving those equations, allows us to construct the equation of circle. So if only two points are given, then these gives two equations with three unknowns. It would be impossible to get three distinct values from two equations. So, there is no possible distinct circle for two points.
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What is the rational zero test used to find rational zeros?
We can use rational zero theorem to find rational zeros.
Given,
Rational zero theorem;-
According to the Rational Zeros Theorem, if P(x) is an integer-coefficient polynomial and is its zero (P() = 0), then p is a factor of P(x constant )'s term and q is a factor of P's leading coefficient (x). The Reasonable Zeros Theorem can be used to locate every rational zero in a polynomial.
Purpose of rational zero test;-
It is also known as the rational root test and the rational zero test. It can be used to locate the polynomial function's zeros. One uses it to determine whether a polynomial has rational zeros or roots. A comprehensive list of the polynomial's potential rational roots is also provided.
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3.75 ÷ 1.50
3
.
75
÷
1
.
50
is equivalent to 375 ÷ 150
375
÷
150
.
The dividend and divisor were both multiplied by .
The quotient of both expressions is?
Both were multiplied by 100 and the quotient of both expressions is 2.5.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
3.75 ÷ 1.50 is equivalent to 375 ÷ 150.
Moving the decimal point 2 places to the right is equivalent to multiplication by 100.
so, both were multiplied by 100.
The quotient is:
3.75 ÷ 1.50 = 2.5
375 ÷ 150 = 2.5
Hence, both were multiplied by 100 and the quotient of both expressions is 2.5.
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Which of the following is the value of the discriminant for 2x² 5x 7 0?
The value of the discriminant for 2x² + 5x + 7 = 0 is -31.
The discriminant of a quadratic equation is the part of the equation used to determine the number and type of solutions. It is calculated by subtracting 4 times the coefficient of the squared term, a, from the coefficient of the linear term, b, squared. This is then divided by four times the coefficient of the squared term, a.
In this case, the equation is 2x² + 5x + 7 = 0.
The discriminant for this equation is calculated as follows:
Discriminant = b² - 4ac
Discriminant = (5)² - 4(2)(7)
Discriminant = 25 - 56
Discriminant = -31
Therefore, the value of the discriminant for 2x² + 5x + 7 = 0 is -31.
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Write an expression to represent: The sum of three and the quotient of a number t and two.
Answer:
3+(t/2) or 3+t/2
Step-by-step explanation:
sum is addition
quotient is division
so, a quotient of T and 2 is t/2 (t divided by 2), and a sum of that and 3 is 3+(t/2)
Adding the parenthesis is optional :)
What is the equation in the slope intercept form of a line passing through the given points 1 and 1 and 3 and 7?
The equation of line in slope intercept form of line passing through the points (1,1) and (3,7) is y = 3x - 2 .
The Slope Intercept form of equation of line is denoted as y = mx + c , where m is the slope and c is y intercept .
the required line passes through the points (1,1) and (3,7) ,
So , the slope(m) is = (7-1)/(3-1) = 6/2 = 3 .
putting the value in slope intercept form , we get ;
1 = 3(1) + c ;
1 = 3 + c ;
c = 1 - 3 ;
c = -2 .
the equation of line will become ⇒ y = 3x - 2 .
Therefore , the equation of the line in slope intercept form is y = 3x - 2 .
The given question is incomplete , the complete question is
What is the equation in the slope intercept form of a line passing through the given points (1,1) and (3,7) ?
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What additional information do you need to prove ∆ ABC ≅ ∆ def by the ASA postulate?
There are some postulates, such as Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side, that can be applied to demonstrate the congruence of triangles.
The Angle-Side-Angle (ASA) postulate asserts that two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
The basic components, primarily the three angles as well as the three sides of a triangle, must be equal to the corresponding angles and sides of the other triangle for two triangles to be congruent.
To demonstrate that the triangle ABC is congruent, we must show that two of its angles and one of its sides are congruent.
If the lengths of the matching sides and angles of two triangles match, the triangles are said to be congruent. In maths, congruence relates to the similarity of two figures in terms of their size and shape. The mirror image of one shape is the same as the other if two shapes are congruent.
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Write the equation of the line containing the points (-2,4) and (-4, 10)
Benjamin threw a rock straight up from a cliff that was 40 ft above the water. If the height of the rock h, in feet, after t
seconds is given by the equation h = - 16t* + 12t + 40, how long will it take for the rock CO hit the water?
Answer:
Step-by-step explanation:
To find the time it takes for the rock to hit the water, we need to find the value of t when h is equal to zero. This is because the rock will hit the water when it reaches a height of zero feet above the water.
Substituting zero for h in the equation h = -16t^2 + 12t + 40, we get:
0 = -16t^2 + 12t + 40
This equation is a quadratic in t, so we can use the quadratic formula to solve for t:
t = (-12 +/- sqrt(12^2 - 4 * (-16) * 40)) / (-32)
Simplifying, we get:
t = (-12 +/- sqrt(144 + 640)) / (-32)
t = (-12 +/- sqrt(784)) / (-32)
t = (-12 +/- 28) / (-32)
t = -40/-32 or t = 16/-32
t = 1/8 or t = -1/2
Since the time cannot be negative (because the rock was thrown upwards), the only solution that makes sense is t = 1/8 seconds.
Therefore, it will take 1/8 seconds for the rock to hit the water.
What is the quotient t?
x-1 is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1
if we equate x-1=0
=> x=1
after putting the value of x=1 in the equation [tex]x^2-2x+1[/tex] to find the remainder.
so the value of [tex]x^2-2x+1[/tex] when x=1
=>1 -2*1 +1
=>0
so the value is 0 which means that x-1 completely divides the given equation [tex]x^2-2x+1[/tex]
since the given equation is quadratic equation and one factor is linear so other factor which is quotient also need to be linear.
let the quotient after division is ax+b
and according to rule of division
[tex]x^2-2x+1[/tex] = (x-1)*(ax+b)
as remainder is 0
so (x-1)*(ax+b) = a[tex]x^2[/tex] +(b-a)x -b
comparing a[tex]x^2[/tex] +(b-a)x -b with [tex]x^2-2x+1[/tex]
we observe that a=1 ,b=-1
so the quotient of the above divsion is x-1
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Complete question:
what is the quotient when [tex]x^2-2x+1[/tex] is divided by x-1
Henrik buys 40 collectible cards per month. Kharif sells 20 cards from his collection of 180 each month. When will Henrik have more cards than Kharif? Show your work.
Henrik will exceed Kharif in the number of cards in the 4th month because in the 4th month Henrik has a total of 160 cards and Kharif has only 100 cards left.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Total cards brought by Henrik per month = 40
Total cards sold by Kharif per month = 20
Total collection of Cards of Kharif = 180
Then,
Let's check after 3 months how many cards both have right now.
Henrik = 3 × 40 = 120
Kharif = 180 - (3 × 20) = 120
It means that after 3 months both are having the same number of cards.
Now, let's check for 4th month,
Henrik = 4 × 40 = 160
Kharif = 180 - (4 × 20) = 100
It means in the fourth month, Henrik will have more cards than Kharif.
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How many odd integers are there from 1 to 100?
There are 50 odd integers from 1 to 100.
What are odd integers?Odd integers are the numbers that cannot be divided by 2 evenly. It cannot be divided into two separate integers evenly. If we divide an odd integer by 2, then it will leave a remainder. In other words, numbers in the form of [tex]2k + 1[/tex], where [tex]k[/tex] ∈ [tex]Z[/tex] (i.e. integers) are called odd numbers.
Calculation:First odd number is 1 from 1 to 100.
Last odd number is 99 from 1 to 100.
Total odd numbers = 99+1 ÷ 2 = 50
There are 50 odd integers from 1 to 100.
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You can work no more than 60 hours each week at your two jobs. Dog walking pays $7 per hour and your sales job at Computers & More, Inc. pays $12 per hour. You need to earn at least $450 each week to pay your bills.
Your friend solves the system of inequalities and tells you that a possible solution is
A possible solution to the system of inequalities is given as follows:
(20,35).
Which means that you work 20 hours dog walking and 35 hours on the sales job at Computers & More, Inc.
How to model the system of inequalities?The variables of the system of inequalities are given as follows:
Variable x: number of hours dog walking.Variable y: number of hours on the sales job at Computers & More, Inc.The number of hours is a countable amount, hence it cannot assume negative values, and the first two conditions are given as follows:
x ≥ 0.y ≥ 0.You can work no more than 60 hours each week at your two jobs, hence:
x + y ≤ 60.
You need to earn at least $450 each week to pay your bills, hence, considering the ratios:
7x + 12y ≥ 450.
Then the solution is obtained from the shaded region of the graph given at the end of the answer.
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Are all equilateral triangles isosceles as well?
4(m - 2) = -2(3m + 3)
Answer:
m=1/5
Step-by-step explanation:
SImplify
4m-8=-6m-6
then 10m=2
so m=1/5
4(m - 2) = -2(3m + 3)
4m - 8 = -6m -6
4m + 6m = -6 + 8
10m = 2
m = 1/5 or 0.2
CHECKING:
4(0.2 - 2) = -2[3(0.2) + 3]
4(-1.8) = -2(0.6 + 3)
- 7.2 = -2(3.6)
- 7.2 = - 7.2
Therefore, the value of m is 1/5 or 0.2. We also proved that this is correct.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-are these good or okayish grades??
Answer:
these are okayish grades but great effort.
What is the formula for the sum of the interior angle measures of a polygon
Answer: (n-2) * 180
Step-by-step explanation:
The formula for the sum of the interior angle measures of a polygon with n sides is (n - 2)180 degrees.
How can we say that the shape or figure are congruent using transformation?
Congruent shapes or figures can be said to be congruent if they can be related to each other by a transformation, such as a translation, rotation, reflection or scaling.
For example, two triangles are congruent if they can be related to each other by a rotation of 180 degrees.
Why is transformation vital and what is it?To establish a student experience that yields significant and equitable improvements in outcomes and educational value, an institution's structures, culture, and business model must be realigned. This process is known as transformation.
How does the transformation process work?Any action or set of actions that takes one or more inputs, changes and adds value to them, and then produces outputs for consumers or clients is referred to as a transformation process.
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Find the volume of this right triangular prism.
5 cm
m
60 cm³
8 cm
b. 90 cm³
C.
120 cm³
d. 150 cm³
Answer:
[tex]Option C) 120cm^{3}[/tex]
Step-by-step explanation:
As we know the formula to find the volume is,
[tex]V=LXBXH[/tex]
[tex]V=5cm x 3cmx8cm[/tex]
[tex]V=120cm^{3}[/tex]
Hope it helps you
HELP ME PLEASE 10POINTS EACH WAIT FOR NEXT QUESTION
Answer:
2/1
Step-by-step explanation:
Answer:
the answer is 2!
Step-by-step explanation:
you count the rise over run
count from where it meets a whole number to where it meets another whole number and then you have your answer!
for this you count from (3,3) to (2,1) which is 2/1 making it 2
Please help I will give brainliest
Answer:
B. 2.2 kilometers
Step-by-step explanation:
⭐What is the change in the cyclist's elevation?
The change in the cyclist's elevation is the value of the height (x) - the value of their starting point (0)Thus, we need to solve for the value of the height (x) of the hill.
Notice that the hill is in the shape of a right triangle. In order to find an unknown side length for right triangles, we need to use a trigonometric function.
⭐What is a trigonometric function?
There are 3 trigonometric functions:sin(θ) = opposite/hypotenusecos(θ) = adjacent/hypotenusetan(θ) = opposite/adjacentθ = an angle measureFirst, let's see what kind of side lengths we are given (opposite, hypotenuse, or adjacent).
We are given a side length of 10km, which is the hypotenuse of the triangle, and we are given a side length of x, which is the opposite of θ (13°).
Therefore, we will use the trigonometric function sin(θ) to solve for x.
Substitute the side lengths and angle measures we are given:
[tex]sin(13) = \frac{x}{10}[/tex]
Set the equation equal to x:
[tex]10sin(13) = x[/tex]
Solve for x. I recommend using a scientific calculator (e.g. Desmos Scientific Calculator):
[tex]2.2 = x[/tex]
∴ The cyclist's change in elevation is 2.2 kilometers.
work out the angle of abc
Answer: The angle is 90 degrees.
Step-by-step explanation:
A triangle that has a diameter as its hypotenuse inside a inscribed circle has a right angle opposite of its hypotenuse. This is true for any right triangle inscribed in a circle, because the equation to get measure B is:
(angle ABC) = 1/2 * (angle AOC)
Angle AOC is 180 degrees. Putting 180 into the euqation, we get 90 degrees for angle ABC.
What is the answer of X² 6x 16?
The answers to the equation x2 – 6x = 16 are x = -2 and x = 8.
What is the answer of x2 6x 16?Two approaches to the equation x2 - 6x = 16 will be examined. First, factoring is used; second, the quadratic formula.
We shall employ the subsequent steps when factoring a solution:
Put all of the terms that are not zero on one side of the equation and zero on the other.
Add the non-zero component of the equation.
Solve the equation by setting each factor to 0.
Getting all non-zero terms on one side of the equation is the first thing want to do.
They are 8x and -2x, respectively. Therefore, (x+8) are the factors of x2 + 6x - 16 = 0. (x-2).
Therefore, the answers to the equation is x2 – 6x = 16 are x = -2 and x = 8.
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How to know what integers and whoke numbers are
Answer:
integers have signs like -&+ while whole numbers are ALWAYS positive
Find the range of the graphed function.
-10
OA. -10 ≤ys 0
OB. y is all real numbers.
O C. -6sys9
O D. y≤0
-10-
10
Based on the graph provided, the range of the function is the set of all real numbers. Therefore, the correct answer is (B) y is all real numbers.
What is a function?Generally, To find the range of a function, you need to find the set of all possible output values of the function.
In this case, the range of the function is given by the set of all y-values that appear on the graph of the function.
The set of all real numbers is considered to represent the range of the function according to the graph that has been supplied. As a result, the response that is accurate is (B), which states that y only contains real values.
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The distance between Eagle and lake and swallow lake on a mob is 9 cm the scale of the map is 14 m equals KM what is the actual distance between Eagle Lake and swallow lake?
The actual distance between Eagle Lake and swallow lake is 9/1400 km.
What is distance?
Distance is the measure of the amount of space between two points or objects. It can be measured in a variety of ways, including miles, kilometers, feet, and meters. Distance is an important concept in physics, mathematics, and many other scientific fields. In addition, distance is a key factor when considering the speed of objects or events. Distance can also be used to measure the time it takes for an object or event to travel from one point to another. Distance is a fundamental concept in understanding the physical universe, and it is essential for navigation, navigation systems, and communication.
The scale of the map is given as,
14 m = 1 Km
We know that, 1 m = 100 cm
So, 14 × 100 cm = 1 Km
1 cm = 1/1400 Km
So, 9 cm = 9 × 1/1400 km
= 9/1400 km.
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Justine just ran her first race. Her distance from the finish line decreased as she ran.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation?
A. justine finished the race in 40 minutes
B. when justine started the race she was 10 kilometers from the finish line
C. after running for 20 minutes justine was 6 kilometers from the finish line
D. justine ran 4 kilometers every 20 minutes
Choices B and C are both correct statements.
Choices A and D are both false.
The y-intercept of the line tells us about the situation when Justine started the race she was 10 kilometers from the finish line.
What are y-intercept and x-intercept?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
Given, a line whose y-intercept is at y = 10 which is represented by the distance remaining in kilometers. Since x shows the time spent running that means at x = 0 she started running.
Therefore, The y-intercept of the line reveals that Justine was 10 kilometers from the finish line when she started the race.
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FILL IN THE BLANK. The domain of f is the _____of f −1, and the _____ of f −1 is the range of f.
As per the concept of inverse function, the domain of f is the range of f⁻¹, and the domain of f⁻¹ is the range of f.
The term inverse function in math is referred as the function y=f(x) can be obtained by switching x and y and solving for y and then the value y will be replaced with f⁻¹ as this denotes the inverse of the function f.
Here we need to find the domain of f is the _____of f⁻¹, and the _____ of f⁻¹ is the range of f.
As we all know that the domain refers the set of all inputs of the function and range refers the set of all outputs of the function.
Based on these definition we have identified that the domain of function is always be the range of inverse function f.
Similarly, the range of inverse function f is always the domain of the function f.
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How many times can you claim SSS sickness benefit?
In a given year, a member may get illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward. For the same condition, the sickness benefit cannot be awarded for more than 240 days.
A daily cash payment is made for each day a member is unable to work as a result of illness or accident.
Qualification Requirements
If a member meets the following criteria, they may be eligible to receive this benefit: Is unable to work due to illness or injury and is confined to a hospital or their home for a minimum of four (4) days;
Has duly notified the SSS directly of the fact of sickness or injury;
Has paid at least three (3) months' worth of payments within the 12-month period immediately preceding the semester of illness or injury.
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What is the equation of this line?
A: y=-2x
B: y = ½x
C: y = -½x
D: y = 2x
Answer:
D
Step-by-step explanation:
when x=1, y should = 2
2(1)=2
so y=2x is correct