Answers
Answer:
[tex]y=x^2+2x-2[/tex]
Step-by-step explanation:
Vertex Form:Vertex form is expressed as: [tex]y=a(x-h)^2+k[/tex], and is super useful when analyzing the vertex, which is given to be (h, k).
Standard Form:Standard form is expressed as: [tex]y=ax^2+bx+c[/tex], and is also useful in certain cases.
Converting Vertex to Standard Form:When converting standard to vertex we have to complete the square to rewrite the equation using a perfect square binomial, which is what really distinguishes the two. Now when we want to convert back into standard form, we simply need to get rid of this perfect square binomial, which we can do by expanding out the perfect square binomial into a trinomial.
So in other words, we want to multiply out the following: [tex](x+1)(x+1)[/tex], which becomes: [tex]x^2+2x+1[/tex] which you can solve by using polynomial multiplication, which is essentially just extending the logic of the distributive property. In general when given two polynomials to multiply, you look at one polynomial, and then multiply it by each term in the other polynomial, now repeat this for each term in the polynomial you were initially looking at. I'll provide a picture to better illustrate this. You can use FOIL if it helps you with multiplying binomials, but remembering how to generally use it, will help you when multiplying polynomials in general.
Now that we've multiplied out the expression, we can substitute it into the equation: [tex]y=x^2+2x+1-3[/tex], now just combine the constants: [tex]y=x^2+2x-2[/tex], and now you've converted it into standard form!
Related Questions
There are a total of 32 books and calculators on a table. The ratio of the number of books to the
number of calculators is 5: 3. How many calculators are on the table?
A. 3
B. 12
C. 20
D. 24
Answers
Answer:
B. 12
Step-by-step explanation:
Your ratio of 5:3 means that the ratio includes 8 objects (5+3). If you multiply the whole ratio by 4, then you have 32 objects on your table. Multiplying your ratio by 4 gives you 5*4 : 3*4 which is 20:12. and since 20 is your amount of books and 12 is your amount of calculators, you have 12 calculators on your table.
BRAINLIEST FOR ANSWER UNDER 10 MINUTES The table shown represents a linear relationship.
x 0 1
3
4
y-8-6-20
Based on the table, what is the equation of the linear relationship in slope-intercept form?
Oy=2x-8
Oy = 2x+8
Oy = -2x + 4
Oy=-2x - 4
Answers
Answer: y = 2x-8
Step-by-step explanation:
Let's try to determine by substitution method. Starting from the first equation:
y = 2x-8
2·0-8 = -8
2·1-8 = -6
2·3-8 = -2
2·4-8 = 0
The first equation satisfies the conditions of the table.
4 3/5+ 2 2/3= l need someone to help me out
Answers
24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
Answers
Answer:
y-int = 0
slope = -1
equation: y = -x
Step-by-step explanation:
The line crosses the y-axis at y = 0, so the y-intercept is 0.
Go from (0, 0) to (-1, 1).
slope = m = rise/run = 1/(-1) = -1
y = mx + b
y = -x
y-int = 0
slope = -1
equation: y = -x
Write the expression as a number in scientific notation.
the quantity 4.2 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity
2.52 × 10−1
2.52 × 101
3.2 × 10−7
3.2 × 107
Answers
On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]
630000/25000
25.2
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Find the coordinates of the circumcenter of the triangle with the given vertices.
L(3,−6), M(5,−3), N(8,−6)
Answers
P(1.6,-2.9) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle?The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.
Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.
Let P(x,y) be the circumcentre of △LMN. Then,
PL = PM = PN
Also, PL² = PM² = PN²
PL² = PM²
(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²
(x-3)² + (y+6)² = (x-5)² + (y+3)²
x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9
4x + 6y = -11 ---- (1)
Also, PM² = PN²
(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²
(x-5)² + (y+3)² = (x-8)² + (y+6)²
x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36
6x - 6y = 27 ---- (2)
Solve (1) and (2) simultaneously by elimination:
6 × (4x + 6x = -11)
4 × (6x - 6y = 27)
24x + 36y = -66
24x - 24y = 108
subtract:
60y = -174
y = -174/60
y = -2.9
Put y = -2.9 into (1):
4x + 6x = -11
4x + 6(-2.9) = -11
4x - 17.4 = -11
4x = 6.4
x = 1.6
Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)
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Why is the discriminant a useful tool to use when solving quadratic equations?
Answers
If d>0, the the quadratic has 2 real solutions
If d=0, the quadratic has one (repeated) solution
If d<0, the quadratic has no real roots.
You must plug d in for these inequalities to determine which one is true, and that will tell you how many solutions a quadratic contains.
Solve the inequality:
4-3x<16
Answers
Answer:
x > -4
Step-by-step explanation:
This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.
Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.
see image.
x > -4.
Step-by-step explanation:1. Write the expression.[tex]4-3x < 16[/tex]
2. Subtract "4" from both sides of the equation.[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]
3. Divide both sides by "-3" and switch the inequality symbol.[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]
Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.
4. Verify.If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).
[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]
That's correct! x > -4 is the correct answer.
The function f(x)= -3x^3 + x^2 +2x rises as x grows very small.
A. True
B. False
Answers
When x is very small (close to 0), the term -3x^3 is much smaller in magnitude than the term x^2. Therefore, the overall value of the function will be dominated by the x^2 term, which is positive. This means that the function will decrease as x becomes very small.
False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.
How to determine the statementFirst, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.
These variables are known as;
The independent variableThe dependent variableThe function f(x) =[tex]-3x^3 + x^2 + 2x[/tex] does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.
Therefore, the function decreases as x grows very small in the negative direction.
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Help me
Like just draw on it
Answers
Answer:
Step-by-step explanation:
(7/8 x 14) / (3/8 x 6) + 2 1/5
Answers
Answer:
7/8 x 14= 12.25 or 49/4 or 12 1/4
(3/8 x 6) + 2 1/5= 4.45
(hope this helps I probably wasn't fully understanding)
A system of linear equations with an infinite number of solutions is a(n) __________ system.
Answers
A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.
Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.
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Solve for -10 - 9/2 x <80
Answers
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
Which object has the largest resultant force?
10N-
10N-
30 N-
A
C
30 N
5N
-5N
10N-
5N-
5N-
5N-
B
D
10N
10 N
Answers
Answer:
To find the resultant force of an object, we need to add up all the forces acting on it. The resultant force is the overall force that the object experiences, taking into account all the individual forces.
In this case, we are given four objects, A, B, C, and D, and the forces acting on them. To find the object with the largest resultant force, we need to calculate the resultant force for each object by adding up all the forces acting on it.
For object A, the forces acting on it are: 10 N, 10 N, and 10 N, for a total of 10 N + 10 N + 10 N = 30 N.
For object B, the forces acting on it are: 5 N, 5 N, 5 N, and 5 N, for a total of 5 N + 5 N + 5 N + 5 N = 20 N.
For object C, the forces acting on it are: 30 N and -5 N, for a total of 30 N + (-5 N) = 25 N.
For object D, the forces acting on it are: 10 N and -5 N, for a total of 10 N + (-5 N) = 5 N.
Therefore, the object with the largest resultant force is object C, with a resultant force of 25 N.
Given f(x)+3f(-x) = 2x+6, find f(x)
Answers
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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which is the highest 4,16,77 and lowest
Answers
Answer:
highest 77 and lowest is 4
What is a b c d and e?
Answers
Answer:
Step-by-step explanation:
help please!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
Not a function
Step-by-step explanation:
A function is when every input(x) has only one output (y). The input 1 has two outputs (0 and 1) so it is not a function.
A person is standing 18 feet from the base of a tree and there's a bird's nest in the tree 10 feet above the ground. what is the angle of elevation from the person to the birds nest? round to the nearest tenth of a degree?
Answers
The angle of elevation from the person to the birds nest is 29^o.
What is angle of elevation?When an object is observed at an angle above the horizontal plane, the angle formed with the horizontal plane with the line of observation is called an angled of elevation. It is measured in degree by a clinometer.
From a sketch of the narration in the given question, we apply the appropriate trigonometric function since the triangle is a right angled triangle.
So, to determine the measure of the required angle of elevation of the bird's nest, we have;
Tan θ = opposite/ adjacent
Tan θ = 10/18
= 0.5556
θ = Tan^-1 0.5556
= 29.05
θ = 29^o
Thus, the angle of elevation from the person to the bird's nest is 29^o.
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A builder buys a 21.5 acres of land to develop a new community of homes and parks.The builder plans to use 0.75 of the land for a park.How many acres will he use for the park?
Answers
He will use 9.375 acres of the land for the park
How to determine how many acres he will use for the park?A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
Since the land is 21.5 acres and 0.75 of the land was used for a park. we can write:
acres used for the park = 0.75 × 12.5 = 9.375 acres
Thus, he will use 9.375 acres for the park
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Latisha plans to purchase her school pictures. The prints cost $108 plus any add-ons she wants to purchase. If she saves $18 per week, which solution represents how many weeks, w, it will take Latisha before she can purchase her school pictures?
Answers
The number of weeks w is given by the equation w = 6 weeks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of weeks be represented as w
The prints cost $108 plus any add-ons she wants to purchase
The amount saved by Latisha per week = $ 18
So , the total amount saved by Latisha for w weeks = 18w
Now , the equation will be
18w = 108 be equation (1)
On simplifying the equation , we get
Divide both sides of the equation by 18 , we get
w = 108 / 18
w = 6 weeks
Therefore , the value of w is 6
Hence , the number of weeks is 6 weeks
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The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.
200.96 square inches
175.84 square inches
100.48 square inches
25.12 square inches
Answers
Answer: D
Step-by-step explanation: 25.12
Answer: The actual answer is (175.84 square inches)
Step-by-step explanation:
First, find the area of the pizza.
You need to use the formula for area of a circle: A = πr^2
or in words, the area of a circle is equal to pi times radius to the second power.
So find the radius which is half the diameter.
The diameter is 16 inches, so the radius is 8 inches.
Now raise 8 to the second power, meaning that you need to times 8 by 8
(8 * 8 = 64) Now you times 64 by pi or 3.14. (64 * 3.14 = 200.96)
That is the area of the entire pizza.
But you still need to find how many square inches are left after 1/8 is eaten.
If 1/8 is eaten, then that means the pizza is divided into eighths.
Take 200.96 and divided that by 8 to find how much the individual pieces are.
200.96/8 = 25.12
But you need to find what is left is the pizza, so times 25.12 by 7 because that is how many pieces are left. 25.12 * 7 = 175.84
Sorry for the long explanation, but here is proof that the answer is correct. I took the same test and got the answer right
Here is a photo from my test:
Have a good day
What is 507 less than 607
Answers
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?
Answers
The number of Dvds owned by Maarissa is 45
How to find the number of dvds?The given parameters that will guide us in finding the number of dvds owned by marissa are
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.
Let the number of dvds owned by Marissa be x
Nymber of dvds owned by Kyle be y
This implies that x+y = 66 ............................1
also, 2y + 3 = x ..................................................2
Substitute x = 2y + 3 in equation 1
= 2y + 3+y =66 Collecting like terms
⇒ 3y = 63
Making y the subject of the relation we have y=21
Recall that 2y + 3 = x
That means x = 2(21) + 3
x=45
Therefore Marrissa owns 45 dvds
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The temperature during the night was -4. In the morning the temperature increased by 3. What is the temperature in the morning
Answers
Answer:
-1
Step-by-step explanation:
Night: -4
Morning: -4 + 3 = -1
Six families went to the food festival. Each family has 2 adults and 4 children. The entry fee for each child ticket costs $4, and an adult ticket costs $8. What would be the total cost of the festival tickets?
Answers
By solving an expression we will see that the total cost for the tickets is $192.
What would be the total cost of the festival tickets?We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:
6*2 = 12 adults in total.
6*4 = 24 children in total.
We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:
12*$8 + 24*$4
That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.
The total cost is then:
12*$8 + 24*$4 = $192
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A triangle has dimensions 9ft by 12ft if you wanted to increase the size of the triangle by a scale factor of 10/3 what would the area of the new triangle be?
Answers
Answer:
The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2
Step-by-step explanation:
To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.
The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.
The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.
Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.
Elaina bought 4.6 pounds of sliced ham at a price of $6.15 per pound. How much did she spend in total? quick
Answers
Answer:
$28.29
Step-by-step explanation:
1 pound: $6.15
4.6 pounds: 6.15 x 4.6 = $28.29
Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline costs $2.76/gallon and the tank takes 15 gallons. You have 2 coworkers who are each willing to pay for a quarter of a tank each month to carpool with you to work. How much do you save each month?
$16.46
$20.70
$15.91
$18.55
Answers
please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee
Answers
1) Note that in the problem above, the complete table is given as:
Team Number: 1 2 3 4 5
Best Jump (ft) 20.6 21.5 20.9 19.4 20.2
2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.
3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.
Why are the Domain and Range Important?Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.
The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.
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