Answer:
17
Step-by-step explanation:
5y-5y^2-5+2+2y+3y^2-1
Answer:
7y - 2y² - 4
Step-by-step explanation:
5y - 5y² - 5 + 2 + 2y + 3y² - 1
5y + 2y - 5y² + 3y² - 5 + 2 - 1 (combine like terms)
7y - 2y² - 4
You purchase x number of balloons for your party. You distribute them evenly among 8 tables. While you are finishing up with your decorations, 2 balloons pop. Is it true that each table will now have x − 2 8/2 balloons? Explain why or why not. someone help plzz
Answer:
No, it's just maximum of two tables that lost balloon so there is no way it affected each table.
Step-by-step explanation:
Number of balloons purchased= x
Number of tables = 8.
Each table has = x/8 balloons
If 2 balloons pop.
Let's assume it's just from a table
That table has( x/8 -2)
If it's from 2 table
The two table has
(X/8-1) for both tables
But the total balloon remaining = x-2
There is no particular equation that can describe the gallon on each table because it's only two balloons that popped.
Answer:
That expression is not true. To evenly distribute the balloons you use x/8. Then you subtract 2 balloons from that total amount. The subtraction must be done after the division. There will not be the same number of balloons at each table.
Step-by-step explanation:
It was the sample answer.
The function f is defined by the following rule
f (x) - 5+1
Complete the function table.
-5
-1
0
2
3
Answer:
The answer to your question is given below.
Step-by-step explanation:
1. f(x) = 5x + 1
x = – 5
f(x) = 5x + 1
f(–5) = 5(–5) + 1
f(–5) = –25 + 1
f(–5) = –24
2. f(x) = 5x + 1
x = – 1
f(x) = 5x + 1
f(–1) = 5(–1) + 1
f(–1) = –5 + 1
f(–1) = – 4
3. f(x) = 5x + 1
x = 1
f(x) = 5x + 1
f(1) = 5(1) + 1
f(1) = 5 + 1
f(1) = 6
4. f(x) = 5x + 1
x = 2
f(x) = 5x + 1
f(2) = 5(2) + 1
f(2) = 10 + 1
f(2) = 11
5. f(x) = 5x + 1
x = 2
f(x) = 5x + 1
f(3) = 5(3) + 1
f(3) = 15 + 1
f(3) = 16
Summary
x >>>>>>>> f(x)
–5 >>>>>> – 24
–1 >>>>>> – 4
1 >>>>>>>> 6
2 >>>>>>> 11
3 >>>>>>> 16
Kelsey had $65 to spend on books. Each book cost $5.50, and there was a $7.50 fee for shipping. She let b equal the number of books she can purchase and wrote the inequality 5.50 b + 7.5 less-than 65 to represent the situation. Which statements describe the reasoning used to determine if Kelsey’s inequality is correct? Select two options. The inequality symbol is correct because she must spend less than $65. The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price. The expression 5.50b + 7.5 is incorrect because $5.50 per book and $7.50 should be combined to $9.50b to determine the total purchase price. The inequality symbol is correct because she cannot spend more than $65.
The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:
The inequality symbol is incorrect because she can spend up to and including $65. The expression 5.50b + 7.5 is correct because $5.50 per book is 5.50b and that is added to the shipping fee of $7.50 to determine the total purchase price.It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.
Based on the information given, the correct expression that can be used to solve the question should be:
65 - (5.50b + 7.5)
In conclusion, the correct options are B and C.
Read related link on:
https://brainly.com/question/16904821
Answer:
B and C
Step-by-step explanation:
prove tan(theta/2)=sin theta/1+cos theta for theta in quadrant 1 by filling in the calculations and reasons. PLEASE HELP!!!!
Answer:
See explanation
Step-by-step explanation:
We have to prove the identity
[tex]tan(\frac{\Theta }{2})=\frac{sin\Theta}{1+cos\Theta }[/tex]
We will take right hand side of the identity
[tex]\frac{sin\Theta}{1+cos\Theta}=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{1+[2cos^{2}(\frac{\Theta }{2})-1]}[/tex]
[tex]=\frac{2sin(\frac{\Theta }{2})cos(\frac{\Theta }{2})}{2cos^{2}(\frac{\Theta }{2})}=\frac{sin(\frac{\Theta }{2})}{cos(\frac{\Theta }{2})}[/tex]
[tex]=tan(\frac{\Theta }{2})[/tex] [ Tan θ will be positive since θ lies in 1st quadrant ]
Corinna has $80. She wants to buy a $256 plane ticket. She will save up her earnings from working at the museum where she earns $16 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $256?
Answer:
80+16h≥256
Step-by-step explanation:
the 80 represents the $80 that Corinna already has
the 16h represents the amount of money made at the museum, with h being the number of hours worked
the inequality symbol is a greater than or equal sign because Corinna must have at least $256 to get the plane ticket, which means you either have to have the exact amount amount or more than the exact amount needed
1. Suzette ran and biked for a total of 80 miles in 9 hours. Her average running speed was 5 miles per hour (mph) and her average biking speed was 12 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution. (a) How many hours did Suzette run? (b) How many hours did she bike?
Answer:
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
Step-by-step explanation:
Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:
Speed = distance / time
The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.
For running:
Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:
5 = p / x
p = 5x
For biking:
Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:
12 = q / y
q = 12y
The total distance ran and biked by Suzette (d) = Distance biked + distance ran
d = p + q
80 = p + q
80 = 5x + 12y (1)
The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run
t = x + y
9 = x + y (2)
Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:
7y = 35
y = 35/7
y = 5 hours
Put y = 5 in equation 2:
9 = x + 5
x = 9 -5
x = 4 hours
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
PLEASE HELP
Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square.
Answer:
perimeter is 4 sqrt(29) + 4pi cm
area is 40 + 8pi cm^2
Step-by-step explanation:
We have a semicircle and a triangle
First the semicircle with diameter 8
A = 1/2 pi r^2 for a semicircle
r = d/2 = 8/2 =4
A = 1/2 pi ( 4)^2
=1/2 pi *16
= 8pi
Now the triangle with base 8 and height 10
A = 1/2 bh
=1/2 8*10
= 40
Add the areas together
A = 40 + 8pi cm^2
Now the perimeter
We have 1/2 of the circumference
1/2 C =1/2 pi *d
= 1/2 pi 8
= 4pi
Now we need to find the length of the hypotenuse of the right triangles
using the pythagorean theorem
a^2+b^2 = c^2
The base is 4 ( 1/2 of the diameter) and the height is 10
4^2 + 10 ^2 = c^2
16 + 100 = c^2
116 = c^2
sqrt(116) = c
2 sqrt(29) = c
Each hypotenuse is the same so we have
hypotenuse + hypotenuse + 1/2 circumference
2 sqrt(29) + 2 sqrt(29) + 4 pi
4 sqrt(29) + 4pi cm
Step-by-step explanation:
First we need to deal with the half circle. The radius of this circle is 4, because the diameter is 8. The formula for the circumference of a circle is 2piR.
2pi4 so the perimeter for the half circle would be 8pi/2.
The area of that half circle would be piR^2 so 16pi/2.
Now moving on the triangle part, we need to find the hypotenuse side of AC. We will use the pythagoram theorem. 4^2+10^2=C^2
16+100=C^2
116=C^2
C=sqrt(116)
making the perimeter of this triangle 2×sqrt(116)
The area of this triangle is 8×10=80, than divided by 2 which is equal to 40.
We than just need to add up the perimeters and areas for both the half circle and triangle.
The area would be equal to 8pi+40
The perimeter would be equal to 4pi+4(sqrt(29))
Use the discriminant to determine the number of real solutions to the equation. −8m^2+2m=0
Answer:
discriminant is b²-4ac
= 2²-4(-8)(0)
= 0
one solution
hope this helps :)
A spinner has 3 red spaces, 5 white spaces, and 1 black space. If the spinner is
spun once, what is the theoretical probability of the spinner NOT stopping on
red?
P(Not red) =
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
If we have 3 red spaces, 5 white spaces, and one blank space, there are a total of 9 spaces.
Since there are 3 red spaces, there is a [tex]\frac{3}{9} = \frac{1}{3}[/tex] chance of getting a red. However, the question asks the probability of not getting a red, so the chances of not getting a red are [tex]1 -\frac{1}{3} = \frac{2}{3}[/tex].
Hope this helped!
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
last option
Step-by-step explanation:
Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
Find the perimeter of the following rectilinear figure.
Answer:
54
Step-by-step explanation
You can't find the other sides, it may seem impossible, but you have to look at this problem in a different way. To find the perimeter of any figure you just need to know the top base, bottom base, right side, and left side.
We see that the top base equals to the bottom base as it is a rectilinear figure. You have to treat the side with 8 and side with 5 as one base. So they equal 13. Now do the same for the bottom.
So, 13 + 13 = 26
The right side is equal to the left side as it is a rectilinear figure, so the right side is 4 + 10 = 14. The left side is also 14.
So 14 + 14 = 28
26 + 28 = 54 units
Sorry, if I couldn't explain properly. I tried my best. As it is hard for me to explain in words. If I could draw it out, I could do better.
Answer:
45
Step-by-step explanation:
I broke the sections apart and then added:
14+14=28
13+13=26
26+28=54
Which of the following best describes the graph shown below?
16
A1
1
14
O A This is the graph of a linear function
B. This is the graph of a one-to-one function
C. This is the graph of a function, but it is not one to one
D. This is not the graph of a function
The vertical line test helps us see that we have a function. Note how it is not possible to draw a single straight line through more than one point on the curve. Any x input leads to exactly one y output. This graph passes the vertical line test. Therefore it is a function.
The function is not one-to-one because the graph fails the horizontal line test. Here it is possible to draw a single straight horizontal line through more than one point on the curve. The horizontal line through y = 2 is one example of many where the graph fails the horizontal line test, meaning the function is not one-to-one.
The term "one-to-one" means that each y value only pairs up with one x value. Here we have something like y = 2 pair up with multiple x values at the same time. This concept is useful when it comes to determining inverse functions.
What the relation of 1/c=1/c1+1/c2 hence find c
[tex]\frac 1c=\frac1{c_1}+\frac1{c_2} [/tex]
$\frac1c=\frac{c_1+c_2}{c_1c_2}$
$\implies c=\frac{c_1c_2}{c_1+c_2}$
3/4a−16=2/3a+14 PLEASE I NEED THIS QUICK and if you explain the steps that would be geat:) Thank youuuuuuu
Answer:
360
Step-by-step explanation:
3/4a - 16 = 2/3a + 14 ⇒ collect like terms 3/4a - 2/3a = 14 + 16 ⇒ bring the fractions to same denominator9/12a - 8/12a = 30 ⇒ simplify fraction1/12a = 30 ⇒ multiply both sides by 12a = 30*12a = 360 ⇒ answerGiven the equations of a straight line f(x) (in slope-intercept form) and a parabola g(x) (in standard form), describe how to determine the number of intersection points, without finding the coordinates of such points. Do not give an example.
Answer:
Step-by-step explanation:
Hello, when you try to find the intersection point(s) you need to solve a system like this one
[tex]\begin{cases} y&= m * x + p }\\ y &= a*x^2 +b*x+c }\end{cases}[/tex]
So, you come up with a polynomial equation like.
[tex]ax^2+bx+c=mx+p\\\\ax^2+(b-m)x+c-p=0[/tex]
And then, we can estimate the discriminant.
[tex]\Delta=(b-m)^2-4*a*(c-p)[/tex]
If [tex]\Delta<0[/tex] there is no real solution, no intersection point.
If [tex]\Delta=0[/tex] there is one intersection point.
If [tex]\Delta>0[/tex] there are two real solutions, so two intersection points.
Hope this helps.
Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.
A) x + y = 109
(1.5)x + 227.50 = (3.5)y
B) x + y = 109
(3.5)x + 227.50 = (1.5)y
C) x + y = 41
(1.5)x + 227.50 = (3.5)y
D) x + y = 109
(1.5)x + (3.5)y = 227.50
E) x + y = 150
(1.5)x + (3.5)y = 227.50
F) x + y = $3.50
(1.5)x + (3.5)y = 227.50
Answer:
[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]
Step-by-step explanation:
Let the items sold with price $1.5 = [tex]x[/tex]
Let the items sold with price $3.5 = [tex]y[/tex]
Initially, total number of items = 150
Items left at the end of the day = 41
So, number of items sold throughout the day = Total number of items - Number of items left
Number of Items sold = 150 - 41 = 109
So, the first equation can be written as:
[tex]\bold{x+y = 109} ....... (1)[/tex]
Now, let us calculate the sales done by each item.
Sales from item with price $1.5 = Number of items sold [tex]\times[/tex] price of each item
= (1.5)[tex]x[/tex]
Sales from item with price $3.5 = Number of items sold [tex]\times[/tex] price of each item
= (3.5)[tex]y[/tex]
Total sales = [tex]\bold{(1.5)x+(3.5)y = 227.50} ....... (2)[/tex]
So, the correct answer is:
[tex]D)\ x + y = 109\\(1.5)x + (3.5)y = 227.50[/tex]
Which line is parallel to line r? line p line q line s line t
Answer:
Line S
Step-by-step explanation:
Answer:
line s
Step-by-step explanation:
coz if you extend both the line (line r and line s )
they will not intersect at any point...
plz let me know if it was helpful to you dude!
NEED ASAP What is the quotient and remainder of 8,595 ÷ 24?
Answer:
358.125
Step-by-step explanation:
Answer:
358 3/24
Step-by-step explanation:
Find the vertex of f(x)= x^2+ 6x + 36
Pls help soon
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
A dress shop bought material for £4.65 a metre and sold it for £6.90 a metre. How much
profit would be made on a roll of 30 metres?
Answer:
£67.50
Step-by-step explanation:
On each metre of material, the shop makes a profit of ...
£6.90 -4.65 = £2.25
So, for 30 metres, the profit will total ...
30 × £2.25 = £67.50
A profit of £67.50 would be made on a 30-metre roll of material.
I need help fast please
Answer:
Difference : 4th option
Step-by-step explanation:
The first thing we want to do here is to factor the expression x² + 3x + 2. This will help us if it is similar to the factored expression " ( x + 2 )( x + 1 ). " The denominators will be the same, and hence we can combine the fractions.
x² + 3x + 2 - Break the expression into groups,
( x² + x ) + ( 2x + 2 ) - Factor x from x² + x and 2 from 2x + 2,
x( x + 1 ) + 2( x + 2 ) - Group,
( x + 2 )( x + 1 )
This is the same as the denominator of the other fraction, and therefore we can combine the fractions.
x - 1 / ( x + 2 )( x + 1 )
As you can see this is not any of the options present, as we have not expanded ( x + 2 )( x + 1 ). Remember previously that ( x + 2 )( x + 1 ) = x² + 3x + 2. Hence our solution is x - 1 / x² + 3x + 2, or option d.
PLEaSE HELP!!!!!! will give brainliest to first answer
Answer:
The coordinates of A'C'S'T' are;
A'(-7, 2)
C'(-9, -1)
S'(-7, -4)
T'(-5, -1)
The correct option is;
B
Step-by-step explanation:
The coordinates of the given quadrilateral are;
A(-3, 1)
C(-5, -2)
S(-3, -5)
T(-1, -2)
The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward
Therefore, we have;
A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)
C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)
S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)
T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)
Therefore, the correct option is B
What is the value of b?
Answer:
55°
Step-by-step explanation:
Perhaps you want the measure of angle B. (There is no "b" in the figure.)
That measure is half the measure of the intercepted arc:
m∠B = 110°/2 = 55°
Angle B is 55°.
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Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 8686 chocolate chip cookies and 42 4242 sugar cookies. Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies. What is the greatest number of identical packages that Shaquira can make?
Answer: 2
Step-by-step explanation:
Given: Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42
Prime factorization of 86 and 42:
86 = 2 ×43
42 = 2 × 3 × 7
GCD of 86 and 42 = 2 [GCD = greatest common factor]
Hence, the greatest number of identical packages that Shaquira can make =2
How do u simplify each expression by combining like terms?
Answer:
1. 8y - 9y = -1y
( 8 - 9 = -1)
3. 8a - 6 +a - 1
( i have showed the like terms here)
8a - 1a= 7a
-6 - 1 = -7
7a - 7
5. -x - 2 + 15x
( i have showed the like terms here)
-x + 15x = 14x
(x = 1)
14x + 2
7. 8d - 4 - d - 2
( i have showed the like terms here)
8d - d = 7d
-4 -2 = -6
7d - 6
8. 9a + 8 - 2a - 3 - 5a
( i have showed the like terms here)
9a - 2a - 5a = 2a
8 - 3= 5
2a + 5
-4.1=8(y-5) it says solve equation
[tex]\text{Solve for y:}\\\\-4.1=8(y-5)\\\\\text{Use the distributive property}\\\\-4.1=8y-40\\\\\text{Add 40 to both sides}\\\\35.9=8y\\\\\text{Divide by 8}\\\\\boxed{4.4875=y}\\\\[/tex]
Complete the square to transform the expression x2 - 2x - 2 into the form a(x - h)2 + k
Answer:
A
Step-by-step explanation:
Find the vertex form of the quadratic function below.
y = x^2 - 4x + 3
This quadratic equation is in the form y = a{x^2} + bx + cy=ax
2
+bx+c. However, I need to rewrite it using some algebraic steps in order to make it look like this…
y = a(x - h)^2 + k
This is the vertex form of the quadratic function where \left( {h,k} \right)(h,k) is the vertex or the “center” of the quadratic function or the parabola.
Before I start, I realize that a = 1a=1. Therefore, I can immediately apply the “completing the square” steps.
STEP 1: Identify the coefficient of the linear term of the quadratic function. That is the number attached to the xx-term.
STEP 2: I will take that number, divide it by 22 and square it (or raise to the power 22).
STEP 3: The output in step #2 will be added and subtracted on the same side of the equation to keep it balanced.
Think About It: If I add 44 on the right side of the equation, then I am technically changing the original meaning of the equation. So to keep it unchanged, I must subtract the same value that I added on the same side of the equation.
STEP 4: Now, express the trinomial inside the parenthesis as a square of a binomial, and simplify the outside constants.
After simplifying, it is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {2, - 1} \right)(2,−1).
Visually, the graph of this quadratic function is a parabola with a minimum at the point \left( {2, - 1} \right)(2,−1). Since the value of “aa” is positive, a = 1a=1, then the parabola opens in upward direction.
Example 2: Find the vertex form of the quadratic function below.
The approach to this problem is slightly different because the value of “aa” does not equal to 11, a \ne 1a
=1. The first step is to factor out the coefficient 22 between the terms with xx-variables only.
STEP 1: Factor out 22 only to the terms with variable xx.
STEP 2: Identify the coefficient of the xx-term or linear term.
STEP 3: Take that number, divide it by 22, and square.
STEP 4: Now, I will take the output {9 \over 4}
4
9
and add it inside the parenthesis.
By adding {9 \over 4}
4
9
inside the parenthesis, I am actually adding 2\left( {{9 \over 4}} \right) = {9 \over 2}2(
4
9
)=
2
9
to the entire equation.
Why multiply by 22 to get the “true” value added to the entire equation? Remember, I factored out 22 in the beginning. So for us to find the real value added to the entire equation, we need to multiply the number added inside the parenthesis by the number that was factored out.
STEP 5: Since I added {9 \over 2}
2
9
to the equation, then I should subtract the entire equation by {9 \over 2}
2
9
also to compensate for it.
STEP 6: Finally, express the trinomial inside the parenthesis as the square of binomial and then simplify the outside constants. Be careful combining the fractions.
It is now in the vertex form y = a{\left( {x - h} \right)^2} + ky=a(x−h)
2
+k where the vertex \left( {h,k} \right)(h,k) is \left( {{{ - \,3} \over 2},{{ - 11} \over 2}} \right)(
2
−3
,
2
−11
).
Example 3: Find the vertex form of the quadratic function below.
Solution:
Factor out - \,3−3 among the xx-terms.
The coefficient of the linear term inside the parenthesis is - \,1−1. Divide it by 22 and square it. Add that value inside the parenthesis. Now, figure out how to make the original equation the same. Since we added {1 \over 4}
4
1
inside the parenthesis and we factored out - \,3−3 in the beginning, that means - \,3\left( {{1 \over 4}} \right) = {{ - \,3} \over 4}−3(
4
1
)=
4
−3
is the value that we subtracted from the entire equation. To compensate, we must add {3 \over 4}
4
3
outside the parenthesis.
Therefore, the vertex \left( {h,k} \right)(h,k) is \left( {{1 \over 2},{{11} \over 4}} \right)(
2
1
,
4
11
).
Example 4: Find the vertex form of the quadratic function below.
y = 5x^2 + 15x - 5
Solution:
Factor out 55 among the xx-terms. Identify the coefficient of the linear term inside the parenthesis which is 33. Divide it by 22 and square to get {9 \over 4}
4
9
.
Add {9 \over 4}
4
9
inside the parenthesis. Since we factored out 55 in the first step, that means 5\left( {{9 \over 4}} \right) = {{45} \over 4}5(
4
9
)=
4
45
is the number that we need to subtract to keep the equation unchanged.
Express the trinomial as a square of binomial, and combine the constants to get the final answer.
Therefore, the vertex \left( {h,k} \right)(h,k) is {{ - \,3} \over 2},{{ - \,65} \over 4}
2
−3
,
4
−65
.
Answer:
(x - 1 )^2 - 3
Step-by-step explanation:
( x - 1 )^2 + ( -3)
x^2 - 2x + 1 - 3
x^2 - 2x - 2
Given the following three points, find by hand the quadratic function they represent.
(-1,-8), (0, -1),(1,2)
(1 point)
Of(x) = -51% + 87 - 1
O f(x) = -3.2? + 4.1 - 1
Of(t) = -202 + 5x - 1
Of(1) = -3.1? + 10.1 - 1
Answer:
The correct option is;
f(x) = -2·x² + 5·x - 1
Step-by-step explanation:
Given the points
(-1, -8), (0, -1), (1, 2), we have;
The general quadratic function;
f(x) = a·x² + b·x + c
From the given points, when x = -1, y = -8, which gives
-8 = a·(-1)² + b·(-1) + c = a - b + c
-8 = a - b + c.....................................(1)
When x = 0, y = -1, which gives;
-1 = a·0² + b·0 + c = c
c = -1.....................................................(2)
When x = 1, y = 2, which gives;
2 = a·1² + b·1 + c = a + b + c...............(3)
Adding equation (1) to (3), gives;
-8 + 2 = a - b + c + a + b + c
-6 = 2·a + 2·c
From equation (2), c = -1, therefore;
-6 = 2·a + 2×(-1)
-2·a = 2×(-1)+6 = -2 + 6 = 4
-2·a = 4
a = 4/-2 = -2
a = -2
From equation (1), we have;
-8 = a - b + c = -2 - b - 1 = -3 - b
-8 + 3 = -b
-5 = -b
b = 5
The equation is therefore;
f(x) = -2·x² + 5·x - 1
The correct option is f(x) = -2·x² + 5·x - 1.
