Answers
now, the picture above does touch the x-axis four times, so it has four roots or x-intercepts or solutions.
So we can see that the roots of it from the graph are, x = -4, x = -2, x = 2 and x = 4, the graph also passes through (0 , -4) down below, now let's reword that.
what's the equation with roots -4 , -2 , 2 and 4 that also passes through (0 , -4)?
[tex]\begin{cases} x = -4 &\implies x +4=0\\ x = -2 &\implies x +2=0\\ x = 2 &\implies x -2=0\\ x = 4 &\implies x -4=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +4 )( x +2 )( x -2 )( x -4 ) = \stackrel{0}{y}} \hspace{5em}\textit{we also know that } \begin{cases} x=0\\ y=-4 \end{cases} \\\\\\ a ( 0 +4 )( 0 +2 )( 0 -2 )( 0 -4 ) = -4\implies 64a=-4 \\\\\\ a=\cfrac{-4}{64}\implies a=-\cfrac{1}{16} \\\\[-0.35em] ~\dotfill[/tex]
[tex]-\cfrac{1}{16}( x +4 )( x +2 )( x -2 )( x -4 ) =y \\\\\\ -\cfrac{1}{16}(x^2+6x+8)(x^2-6x+8)=y\implies -\cfrac{1}{16}(x^4-20x^2+64)=y \\\\\\ ~\hfill~ {\Large \begin{array}{llll} -\cfrac{x^4}{16}+\cfrac{5x^2}{4}-4=y \end{array}}~\hfill~[/tex]
Check the picture below.
Related Questions
A local car dealership is offering a sale. All new cars are on sale for 23% off the sticker price. All used cars are 10% off the sticker price. You have narrowed your decision down to two cars:
Car 1 (new) sticker price = $20,000.00
Car 2 (used) sticker price = $17,000.00
Answer the following questions.
How much money would you save on car 1?
How much money would you save on car 2?
Which car would you choose to buy and why? Justify your answer using your calculations.
Answers
To find out how much money you would save on car 1, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $20,000.00 x 0.23 = $4,600.00. So you would save $4,600.00 on car 1.
To find out how much money you would save on car 2, you would multiply the sticker price by the discount percentage (expressed as a decimal). In this case, that would be $17,000.00 x 0.10 = $1,700.00. So you would save $1,700.00 on car 2.
Based on the calculations, Car 1 would be a better deal. Even though Car 2 is cheaper by $3,000.00 before discount, Car 1 saves more on discount of $4,600.00 compared to Car 2's $1,700.00. So Car 1 would be more affordable overall.
If x is 0, wouldn't that make it 2^0 being one
Answers
Answer:
any number raised by power 0 is always one
ie 10000000000^0 = 1
99999999^0 =1
23^0 = 1
Answer:
Yes. If x=0, then 2ˣ = 0
Step-by-step explanation:
I presume you mean 2ˣ
Any number raised to the power zero is 1 so if x = 0, 2⁰ = 1. There are debates about what 0⁰ evaluates to but I don' think you need to worry about that for this question
I hope I interpreted your question correctly.
Solve for x.
2(x−3 1/2)=10 3/4
Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
x = 71/8
Step-by-step explanation:
Solve for x:
2 (x - (3 + 1/2)) = 10 + 3/4
Put 3 + 1/2 over the common denominator 2. 3 + 1/2 = (2×3)/2 + 1/2:
2 (x - (7/2)) = 10 + 3/4
2×3 = 6:
2 (x - (1/2 6 + 1/2)) = 10 + 3/4
6/2 + 1/2 = (6 + 1)/2:
2 (x - (7/2)) = 10 + 3/4
6 + 1 = 7:
2 (x - 1/2 7) = 10 + 3/4
Put each term in x - 7/2 over the common denominator 2: x - 7/2 = (2 x)/2 - 7/2:
2 ((2 x)/2 - 7/2) = 10 + 3/4
(2 x)/2 - 7/2 = (2 x - 7)/2:
2 (1/2 (2 x - 7)) = 10 + 3/4
(2 (2 x - 7))/2 = 2/2×(2 x - 7) = 2 x - 7:
(2 x - 7) = 10 + 3/4
Put 10 + 3/4 over the common denominator 4. 10 + 3/4 = (4×10)/4 + 3/4:
2 x - 7 = ((4×10)/4 + 3/4)
4×10 = 40:
2 x - 7 = 40/4 + 3/4
40/4 + 3/4 = (40 + 3)/4:
2 x - 7 = ((40 + 3)/4)
40 + 3 = 43:
2 x - 7 = 43/4
Add 7 to both sides:
2 x + (7 - 7) = 43/4 + 7
7 - 7 = 0:
2 x = 43/4 + 7
Put 43/4 + 7 over the common denominator 4. 43/4 + 7 = 43/4 + (4×7)/4:
2 x = (43/4 + (4×7)/4)
4×7 = 28:
2 x = 43/4 + 28/4
43/4 + 28/4 = (43 + 28)/4:
2 x = ((43 + 28)/4)
43 + 28 = 71:
2 x = 71/4
Divide both sides by 2:
x = (71/2)/4
4×2 = 8:
Answer: x = 71/8
Which of the following quadratic equation describe the speed of Raj’s car
Answers
The quadratic equation that describe the speed of Raj's car is c) x² + 5x - 500 = 0
How to calculate the equation?speed of raj car = x km/h .
speed of ajay car = 5 km faster than speed of raj car = (x + 5) km/h .
Distance cover by ajay in 2 hours = 2(x + 5) km
time taken by raj to cover 400 km = D/S = (400/x) hours .
time taken by ajay to cover 400km = D/S = 400/(x + 5) hours .
A/q,
400/x - 400/(x + 5) = 4
400{1/x - 1/(x + 5)} = 4(x + 5 - x)/x(x + 5) = 1/100
x² + 5x = 5 * 100
x² + 5x - 500 = 0
In this case, it should be noted that the concept that was Illustrated here is the concept of quadratic equations.
Therefore, based on the calculation above, the correct option is C.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ1
Complete question
Which of the following quadratic equation describe the speed of Raj's car?
a) x² - 5 X - 500 = 0
b) x² + 4x - 400 = 0
c) x² + 5x - 500 = 0
d) x² - 4x + 400 = 0
Pls help 4 cups of flour are mixed with 24 cups of sugar. How many cups of flour should be used if 84 cups of sugar are used?
Answers
The amount of flour needed for 84 cups of sugar will be 14 cups of flour.
How to measure quantity?A property that can be measured like, mass, length, time, volume, and pressure. A unit is a standard quantity against which a quantity is measured for example, gram, metre, second, litre, pascal, which are units of the preceding quantities.
To measure the quantity of cups of flour needed to mix 84 cups of sugar;
24 cups of sugar = 4 cups of flour
84 cups of sugar = ? cups of flour = 84/24 x 4
for 84 cups of sugar = 3.5 x 4 = 14 cups of flour.
It will take 14 cups of flour to mix 84 cups of sugar.
Learn more on measurement here: https://brainly.com/question/4805425
#SPJ1
Why is 47 a prime number?
Answers
Answer:
47 is a prime number because it has only two factors, 1 and 47.
Step-by-step explanation:
Your welcome.
Answer: A prime number is a number that can only be divided evenly by 1 and itself. 47 is a prime number because it can only be divided evenly by 1 and 47. It cannot be divided evenly by any other number. That's why we say 47 is a prime number. ✅
PLEASE MAKE THIS A BRANLIEST ANSWER!!!
for questions 13-16, determine if the inverse of the function shown on the graph would also be a function.
Answers
If a function yields the result y, then its inverse function, denoted by the symbol , will return the value x.
What is meat by inverse of the function?A function's output is returned when its inverse function does the same action variable. The inverse function of a function, or f-1(y), will return the value x if the function f(x) produces the output y.A function that reverses the action of a function, or f, is known as its inverse in mathematics.
Here,
A function that reverses the effects of another function is said to have an inverse. If y = f(x), then x must always equal g, then a function g is the inverse of a function f. (y). Application of f followed by application of g is equivalent to doing nothing, in other words. As g(f(x)) = x, this can be expressed in terms of the relationship between f and g.
Because they allow for the reversal of mathematical operations, inverse procedures are crucial for solving equations (e.g. logarithms, the inverses of exponential functions, are used to solve exponential equations). How to invert a mathematical technique is one of the most crucial questions whenever one is introduced.
To learn more about inverse function refer to;
brainly.com/question/3831584
#SPJ1
The complete question : " In Exercises 15-18, match the graph of the function with the graph of its inverse function. [The graphs of the inverse functions are labeled (a), (b), (c), and (d).]"
Which of the following is logically equivalent to~ (~p⇒q)?p ∧qp ∧~ q~p ∧q~ p ∧~q
Answers
p ∧qp ∧~ q~p ∧q~ p ∧~q is logically equivalent to~ (~p⇒q) for the given question
If p → q
and q →r , then you can use the law of transitivity to conclude
q→r.
That is a basic law of sillogisms.
An example will help you to understand the transivity law:
Make p, stand for 3 > 3/4, q stand for 3/4 > 15 / 20, the you can conclude that 3 > 15 / 20.
3 > 3/4
3 /4 > 15 / 20
Then, 3 > 15 /20.
This is, from the fact that you know that 3 is gretar than 3/4 and that 3/4 is greater than 15/20, you can conclude that 3 > 15 / 20. That is transitivity and is a law of logic, which you can use to get conclusions.
learn more about of logically equivalent here
https://brainly.com/question/8499637
#SPJ4
Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5
Answers
The figure's scale factor and type of dilatation are
enlargement using a 2.5 scale factorFinding the type of dilatationWhat are scale factors?Scale factors are applied to alter the size of the image. The circumstance of increase is frequently referred to as enlargement or magnification.
Given that the preimage is smaller than the image, the situation is enlargement. This implies that the scale factor will also be higher than 1.
Establishing a baseline, say side 8 and side 20 in the preimage and the image respectively. Then, assuming the factor is k, get the factor.
8k = 20
k = 20/8
k = 2.5
The scale factor is 2.5
Read more on scale factor here:
brainly.com/question/8159270
#SPJ1
The formula for the area of a square is A = s^2 where s is the side length. A square garden has a side length of x^4y. What is the area of the garden?
Answers
What happens when you take the absolute value of a complex number?
Answers
The origin in the complex plane is represented by the number 0. Therefore, the separation between a complex number and the complex plane's origin (zero) equals its absolute value.
What happens when you calculate a number's absolute value?A number, variable, or expression is enclosed in two vertical bars to represent an absolute value in mathematics, as in the following example: A number's absolute value is always either positive or zero when calculated. The absolute value remains the same whether the initial value is already positive or zero.The origin in the complex plane is represented by the number 0. Therefore, the separation between a complex number and the complex plane's origin (zero) equals its absolute value.You won't have a solution if your absolute value expression is set to a negative quantity.To learn more about absolute value refer to:
https://brainly.com/question/24368848
#SPJ4
The cost of 1 cap and 1 wallet is
£28.
The cost of 2 caps and 1 wallet is
£45.
a) How much does 1 cap cost?
b) How much does 1 wallet cost?
Answers
Answer:
cap: 17, wallet: 11
Step-by-step explanation:
45 - 28 = 17
45 - (17 x 2) =
45 - 34 = 11
could also do:
28 - 17 = 11
Hope this helps have a good day
I kinda need help :<
For each coordinate grid, identify a pair of congruent figures. Then determine a congruence transformation that maps the pre-image to the congruent image.
Answers
The coordinates of the vertices of △ABC are A(-4,1), B(-2,4), C(-2,0), △CDE are C(-1,-1), D(1,1), E(4,-1), and △IHG are I(2,3),H(4,0), G(4,4).
The transformation is △ABC reflected with the line y =2 and shifted 6 units right sides.
What are the vertices of a triangle?
A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
There are three triangles. The vertices of △ABC are A(-4,1), B(-2,4), C(-2,0).
The vertices of △CDE are C(-1,-1), D(1,1), E(4,-1). The vertices of △IHG are I(2,3),H(4,0), G(4,4).
The △ABC is congruent with △IHG.
The difference between the x-coordinate of A and I is (2 - (-4)) = 6
The difference between the x-coordinate of B and H is (4 - (-2)) = 6
The difference between the x-coordinate of C and G is (4 - (-2)) = 6
The sum of the y-coordinate of A and I is (3+1) = 4
The sum of the y-coordinate of B and H is (4 + 0) = 4
The sum of the y-coordinate of C and G is (4 + 0) = 4
The midpoint of y-coordinate of △ABC and △IHG is 4/2 = 2
The △ABC is reflected by y = 2 and shifted 6 units right side.
To learn more about transformation, click on the below link:
https://brainly.com/question/29186141
#SPJ1
A food delivery driver is 4 3/4 miles west of a city's library when he receives a call to pick up food from a restaurant. The restaurant is 1.5 miles east of the library. Assume the driver takes the most direct route to the restaurant. How will the driver drive to the restaurant? Select from the drop-down menus to correctly complete the statement.
Answers
If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.
What is a fraction?The numerator, which is the portion of a fraction that is at the top, and the denominator, which is the portion that is at the bottom, are its two constituent parts.
It is given that:
A food delivery driver is 4 3/4 miles west of a city library when he receives the call to pick up food from a restaurant.
The restaurant is 1.5 miles east of the library.
The mixed fraction can be written as:
4 3/4 = 19/4 = 4.75
Total = 4.75 + 1.50 = 6.25 miles
Thus, If a food delivery driver is 4 3/4 miles west of a city library when he gets a call to pick up food from a restaurant, the mixed fraction is 4.75 miles, and the overall distance is 6.25 miles.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ1
Help me with this please
Answers
Answer:
Step-by-step explanation:
All except "E", "C", and "B".
A and D are true.
The line is negative and the slope is -5, not 5.
Estimate a 15% tip on a dinner bill of 32.57 by first rounding the bill amount to the nearest ten dollars.
(Timed, but you will get a lot of points and brainliest and 5 stars!)
Answers
Answer: 5.
Step-by-step explanation: The .57 doesn't matter so we can remove that.
Multiply 32 by 0.15
32 x 0.15 = 4.8
After you get your result, round it to the nearest tenths.
4.8 = 5
hope this helps
Evaluate each expression when X=3/4 and y=2.5
1. 8x
2. y2
3. 10/y
Answers
Answer:
1. 6
2. 5
3. 4
Step-by-step explanation:
For each expression, Substitute the variable for what is given in the statement.
1. 8×(3/4)=6
2. 2.5×(2)=5
3. 10/2.5=4
Write the quadratic equation whose roots are -3 and 6, and whose leading coefficient is 4
Answers
The quadratic equation whose roots -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0
What is quadratic equation?A quadratic equation is an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0. Examples of quadratic equations include all of these: y = x² + 3x + 1 , y = x²+x-1
If the root of the quadratic equation are -3 and 6
then, x = -3 and x= 6
therefore x+3 = 0 and (x-6) = 0
(x+3)(x-6) = 0
with leading coefficient 4,
then 4( x+3) ( x-6) = 0
4 ( x²-6x+3x-18) = 0
4( x²-3x-18) = 0
open the parentheses,
4x²-12x-72 = 0
Therefore, the quadratic equation with root -3 and 6 and leading coefficient 4 is 4x²-12x-72 = 0
learn more about quadratic equation fromhttps://brainly.com/question/1214333
#SPJ1
(40 PTS, HELP ME) In the following diagram, A || B.
Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for x.
Solve for x, showing all of your work
Answers
The answer is 24
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.
Given here: A || B.
Now if transversal D intersects A and B we have
If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
Thus we have 4x+5+3x+7=180
7x=168
x=24
Hence, The value of x is 24
Learn more about supplementary angles here:
https://brainly.com/question/13045673
#SPJ1
To change the weight of kilograms into pounds, multiply the weight in kilograms by ____________
Answers
To change the weight of kilograms into pounds, multiply the weight in kilograms by 2.2
According to the conversion systems, 1 kg = 2.2046 lbs
To facilitate conversion on a pen-paper basis we cannot use 2.2046 whole.
Hence we generally consider 1 k = 2.2 pounds.
The symbol for pounds is lbs and for kilograms is kg.
Now, 1 kg is 2.2 lbs
2 kg = 1 kg + 1 kg
= 2.2 lbs + 2.2 lbs
= 4.4lbs = 2 X 2.2
3 kg = 1 kg + 2 kg
= 2.2 lbs + 4.4 lbs
= 6.6 lbs. = 3 X 2.2
Hence we can see that for all these numbers we can multiply 2.2 to the given weight in kg to get the pounds form.
Hence we need to multiply 2.2
To learn more about Conversion visit
https://brainly.com/question/24210516
#SPJ4
Solve the system of linear equations by elimination.
-5x+12y=8
2x-8y=0
Answers
Answer:
x = -4
y = -1
Step-by-step explanation:
-5x+12y=8
2x-8y=0
We multiply the first equation by 2 and the second equation by 5
-10x + 24y = 16
10x - 40y = 0
-16y = 16
y = -1
Now put -1 back in for y and solve for x
-5x + 12(-1) = 8
-5x - 12 = 8
-5x = 20
x = -4
Let's check
-5(-4) + 12(-1) = 8
20 - 12 = 8
8 = 8
So, x = -4 & y = -1 is the correct answer.
I need helppp quickkkk
Answers
The required triangles are similar because Corresponding sides of the triangles are proportional and their corresponding angles are same.
What is Similarity?For plants, an isotype is a replica of the logotype; holotype and isotypes are frequently taken from the same individual plant or samples from the same collection. Hence Isotypes are pairs of related holotypes. Therefore, choice D is the right response.
According to question;To prove the similarity of two triangles,Corresponding sides of the triangles are proportional and their corresponding angles are same.
The scale factor of their side = 33/11 = 3
So, ΔQRS ~ ΔTUV with scale factor of 3.
To know more about Similarity visit:
brainly.com/question/26451866
#SPJ1
Since the respective sides of the required triangles are proportional and their corresponding angles are identical, the required triangles are similar.
What exactly is similarity?Holotype and isotypes are typically obtained from the same specific plant or samples from the same collection. An isotype is a copy of the logotype for plants. Since they are related holotypes, isotypes are pairs of them. D is the appropriate response, thus.The respective sides of the triangles are proportional, and their corresponding angles are identical, which helps to demonstrate how similar two triangles are.Their side's scale factor is 33/11, or 3.As a result, QRS TUV with a scale factor of 3.To learn more about isotypes refer
brainly.com/question/26451866
#SPJ1
Which question can be answered by finding 4
You have 4 pounds of fruit and use pound. How much fruit is remaining?
How much is of 4 pounds of fruit?
CLEAR
You are buying pound containers of fruit at the store. How many containers do you need to buy to have 4 pounds of truit?
Answers
The question which can be answered by finding 4½ ÷ ¼ is "You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?".
The correct answer choice is option C
How to divide fraction?You have 4½ pounds of fruit and use ¼ pound. How much fruit is remaining
Pounds of fruits remaining = Pounds of fruits you have - pounds of fruits used
= 4½ - ¼
= 9/2 - 1/4
= (18-1)/4
= 17/4 pounds
How much is ¼ of 4½ pounds of fruit?
= ¼ × 4½
= ¼ × 9/4
= 9/16 pounds of fruits
You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?
Number of containers needed = 4½ ÷ ¼
= 9/2 ÷ 1/4
multiply by the reciprocal of 1/4
= 9/2 × 4/1
= 36/2
= 18 containers
Hence, The question which represents 4½ ÷ ¼ is "You are buying ¼ pound containers of fruit at the store. How many containers do you need to buy to have 4½ pounds of truit?".
Read more on division of fraction:
https://brainly.com/question/1622425
#SPJ1
ASAPPPP I'LL GIVE BRAINIESTβ
In each basket of fruit, there are 3 more apples than pears.
Which equation represents the relationship between the number of apples a and the number of pears p?
p = a + 3
p, = , a, + 3
a = p + 3
a = p + 3
p = 3a
p, = 3, a
a = 3p
Answers
The equation that represents the relationship between the number of apples a and the number of pears p is b. a = p + 3.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
From the information, in each basket of fruit, there are 3 more apples than pears.
Let p = pears
Let a = apple
Therefore, the equation that represents the relationship between the number of apples a and the number of pears p is a = p + 3.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
What is the exponential form of 64 *?
Answers
The exponential form of 64 is 2^6.
what is the answer please i need help -2.6f+0.4f-14-4
Answers
Answer: [tex]-2.2f-18[/tex]
Step-by-step explanation:
[tex]-2.6f+0.4f-14-4=f(-2.6+0.4)+(-14-4)=-2.2f-18[/tex]
Can someone explain how to solve this
Answers
Answer:
(-(11 w^2 - 13))
Step-by-step explanation:
Simplify the following:
2 w^2 - 13 w^2 + 13
Grouping like terms, 2 w^2 - 13 w^2 + 13 = (-13 w^2 + 2 w^2) + 13:
(-13 w^2 + 2 w^2) + 13
2 w^2 - 13 w^2 = -11 w^2:
-11 w^2 + 13
Factor -1 out of -11 w^2 + 13:
Answer: (-(11 w^2 - 13))
Solve for y
x = x (2x - 4) + y
The first x is squared I just can’t put a square in brainly
Answers
Answer:
y = −x^2 + 4x
Step-by-step explanation:
x^2 = x (2x - 4) + y
Let's simplify it and we get
x^2 = 2x^2 - 4x + y
Now, we want to get the y by itself
x^2 = 2x^2 - 4x + y
-x^2 = -4x + y
-x^2 + 4x = y
So, our answer is y = −x^2 + 4x
Is 48 a factor of 8?
Answers
No, number 48 is not the factor of 8 , 48 is a multiple of 8.
As given in the question,
Given number is equal to ,
48.
Factors are those numbers which divide the given number completely without leaving any remainder.
The factors of the number 48 are equal to:
1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Multiple of 8 are equal to :
8, 16, 24, 32, 40, 48, .....
48 is not considered as a factor of 8 it the multiple of the number 8.
8 is the factor of the given number 48.
Therefore, number 48 is not the factor of 8 , it is considered as the multiple of 8.
Learn more about factors here
brainly.com/question/26923098
#SPJ4
What is the range of f(x) = |x| − 5?
Answers
Answer:
from -5 to infinity
Step-by-step explanation:
Hope this helps.