Determine the corresponding general form of each of the following vertex form
1. y = (x– 1)2
A. y = x2+ x + 1
B. y = x2 – 2x – 1
C. y = x2 – 2x + 1
2. y = (x + 4)2– 5
A. y = x2+ 8x – 11
B. y = x2+ 8x – 21
C. y = x2+ 8x + 21
3. y = -(x + 9)2– 10
A. y = -x2– 18x + 91
B. y = -x2– 18x – 91
C. y = -x2– 18x – 71
4. y = 3(x + 2)2– 18
A. y = 3x2+ 12x – 6
B. y = 3x2+ 12x + 6
C. y = 3x2+ 12x – 14
5. y = -2(x + 1)2– 16
A. y = -2x2– 4x – 18
B. y = -2x2– 4x – 2
C. y = -2x2– 4x – 14
6. y = 5(x + 5)2
A. y = 5x2+ 50x + 125
B. y = 5x2+ 50x + 25
C. y = 5x2+ 25x + 125
7. y =1/2(x + 8)2– 8
A. y = 1/2x2 + 8x + 24
B. y= 1/2x + 8x – 40
C. y = 1/2x2 + 16x + 24
8. y = (x + 3/2)2 + 3/4
A. y = x2+ 3x + 2
B. y = x2 + 6/4x + 12/16
C. y = x2 + 3x + 3
9. y = 2(x + 8)2– 5x
A. y = 2x2 + 32x + 59
B. y = 2x2 + 27x + 128
C. y = 2x2+ 37x + 64
10. y = -5(x – 4)2+ 15
A. y = -5x2+ 40x – 65
B. y = -5x2 – 40x – 65
C. y = -5x2+ 40x + 65
Answer:
Step-by-step explanation:
(a + b)² =a² + 2ab + b²
(a -b)² = a² - 2ab + b²
1) y = (x -1)²
y= x² - 2*x*1 + 1
y = x² - 2x + 1
Ans: C
2)y = (x +4)² + 5
y = x² +2*x*4 + 4² + 5
= x² + 8x + 16 + 5
y = x² + 8x + 21
C
3) y = -(x + 9)²- 10
y = - [x² + 18x + 81] - 10
= -x² - 18x - 81 - 10
y =-x² - 18x - 91
B
4) y = 3(x + 2)² - 18
y =3 [x² + 4x + 4] - 18
y = 3x² + 12x + 12 - 18
y =3x² + 12x - 6
A
5) y = -2(x + 1)² - 16
= -2[x² + 2x + 1] -16
= -2x² - 4x - 2 - 16
y = -2x² - 4x - 18
A
6) y = 5(x + 5)²
=5[x²+ 10x + 25]
y = 5x² +50x + 125
A
7)y = (1/2)(x + 8)² - 8
y = (1/2) (x² + 16x + 64) - 8
[tex]y = \dfrac{1}{2}*x^{2}+ \dfrac{1}{2}*16x + \dfrac{1}{2}*64 -8\\\\\\y =\dfrac{1}{2}x^{2}+8x +32 - 8\\\\\\y=\dfrac{1}{2}x^{2} +8x + 24[/tex]
A
8) y = (x + 3/2)² + 3/4
[tex]y = x^{2} +2*x*\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{3}{4}\\\\y=x^{2}+3x+\dfrac{12}{4}\\\\\\y=x^{2}+3x + 3[/tex]
C
9) y = 2[x² + 16x + 64] - 5x
y = 2x² + 32x + 64 - 5x
y =2x² + 27x + 6
the following are polynomials EXPECT
Answer:
where the numbers at???
Step-by-step explanation:
What is the slope of the line passing through the points (−3, 4) and (2, −1)?
3/5 this is a fraction by the way
1
−1
−53
[tex](x_1,y_1) = (-3,4),~~ (x_2,y_2) = (2,-1)\\\\\text{Slope,}~ m = \dfrac{y_2 - y_1}{x_2 - x_1} =\dfrac{-1-4}{2+3} = \dfrac{-5}5 = -1[/tex]
Aaden wants to get a subscription to an online library. There are two subscription options, one of which charges a fixed 96 dollar annual fee and the other which charges 3 dollars per book he borrows.
Here's a graph that shows a system of equations for this scenario where x is the number of books Aaden borrows and y is the total cost of the subscription.
A graph with two lines and a point. Line A is labeled y equals 96. Line B is labeled y equals 3 times x. Point S is below line B and above line A.
What does point SSS represent in this context?
Choose 1 answer:
(Choice A)
A
A number of books and their cost using the subscription that charges per book
(Choice B)
B
A number of books and their cost using the subscription with the annual fee
(Choice C)
C
A number of books and their cost where both subscriptions cost the same
(Choice D)
D
A number of books and their cost that is not possible with either subscription
I sent a screen shot of the graph
Answer:
A
Step-by-step explanation:
A number of books and their cost where the subscription with the annual fee costs less. hope it helps and take care ✌
Point S represents the number of books and their cost using the subscription that charges per book
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Based on the given graph, point S represents the number of books and their cost using the subscription that charges per book (Option A).
This is because point S is located below line B, which represents the total cost of the subscription with a variable cost per book, and above line A, which represents the total cost of the subscription with a fixed annual fee.
Therefore,
Point S represents a combination of a certain number of books borrowed and the corresponding total cost of the subscription using the variable cost per book option.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Question 1 of 10
If f(x) = 4x - 12, what is f(2)?
A. -20
ОО O
B. 8
C. -4
O
D. 4
Answer:
C -4
Step-by-step explanation:
f(2)= 4(2) - 12
f(2) = -4
The sum of the interior angles in a polygon is 15,480°. Calculate the number of sides in the regular polygon.
If
x
=
2
and
y
=
6
, evaluate the following expression:
3
(
3
y
−
4
x
)
12. Hannah wants to buy 4 presents for at least $60. She wants to spend an equal amount of money on each present. Write and solve an inequality to show the least amount of money Hannah will spend on each present
Answer: 15
Step-by-step explanation:
So it is pretty much 60/4 which is easy 15 here is the work
1 5
4 6 0
- 4
2 0
- 2 0
0
Answer:
x ≥ $15
Step-by-step explanation:
At least means ≥
4x ≥ $60 Replace the inequality sign with an = sign and solve the equation.
4x = $60
x = $60 ÷ 4
x = $15 Now put the inequality sign back into the problem
x ≥ $15
Dan earns £7.90 per hour. How much will he earn for 6 hours work?
Answer:
$47.4
Step-by-step explanation:
Answer:
Step-by-step explanation:
The earning will increase for 6 hours. So, we have to multiply 7.90 by 6
Earnings after 6 hours = 6 * 7.90 = £ 47.40
Use the following function rule to find f(2).
f(x) = 2^x
f(2) =
Answer:
4
Step-by-step explanation:
2²
4PLEASE MARK ME AS BRAINLIST3. Given: DE is a midsegment of AABC. Show all work.
a. Find the value of x and y.
b. What is the length of AC?
Answer:
x = 10
y = 1
DE = 7
AC = 14
Step-by-step explanation:
x + 2 = 24/2
x = 12 - 2
x = 10
y + 6 = x - 3
y = 10 - 3 - 6
y = 1
13, 22,31,... what is the 31st term?
Answer:
thirty-first ordinal. being or denoting a numerical order in a series.
Step-by-step explanation:
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
ab+4a-3b-12 = (b+4)(_____)
what's the slope and y-intercept for -30+10y=-2x ?
Answer:
XDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
LOL
What is the equation of the line from the graph?
Answer:
y=3
Step-by-step explanation:
All points have the same y coordinate. Or
A line parallel to the x axis has slope 0, so it's y= 0x +3 that becomes y=3
Answer: Y=3
Step-by-step explanation:
!!!!5 step plan!!!!!
The width of a rectangle is 5 cm more than twice the length the perimeter is 56 cm find the dimensions of the rectangle
Answer: W = 20 1/3, L = 7 2/3 cm
Step-by-step explanation:
Width, W, is 5 cm more than twice the length of the perimeter.
Perimeter = 2W + 2L
W = 2L+5
Perimeter is 56cm:
56 cm = 2W + 2L
Substitute W = 2L + 5 for W:
56 cm = 2W + 2L
56 cm = 2(2L+5) + 2L
56 cm = 4L + 10 + 2L
6L = 46 cm
L = 7 2/3 cm
Since W = 2L + 5
W = 2(7 2/3) + 5
W = 2 (23/3) + 5
W = 46/3 + 5
W = 15 1/3 + 5
W = 20 1/3
2W + 2L = P?
2(20 1/3) + 2(7 2/3) =56 ?
40 2/3 + 15 1/3 = 56?
56 = 56 YES
What is the rate of change?
Answer:5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
19-14 = 5
24 - 19 = 5
29 - 24 = 5
and so on
I hope this helps!
A teacher needs 35 model rockets for his students. Model rockets are sold in boxes of 3, boxes of 5, and boxes of 7. Which boxes could the teacher buy so he has no leftover rockets?
Write the slope- intercept form of the equation
What is the measure of
Answer:
∠ ABC = 108°
Step-by-step explanation:
The 2 given angles are vertically opposite and are congruent , that is
4x + 8 = 3x + 33 ( subtract 3x from both sides )
x + 8 = 33 ( subtract 8 from both sides )
x = 25
Then
∠ ABC = 3x + 33 = 3(25) + 33 = 75 + 33 = 108°
If the price of a particular chocolate bar is increased by 40%, and it used to be $2, what is the new price after the increase?
Answer:
6$
Step-by-step explanation:
2+4=6
20%+40%=60%
The new price after the increase is $2.8 .
What is percent increase?Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.
According to the question
The price of chocolate bar = $2
The price of a particular chocolate bar is increased by 40%,
i.e
The percent increase in the price of chocolate bar = 40%
Now,
increase prize :
= [tex]2*\frac{40}{100}[/tex]
= $0.8
The new price after the increase
= $2.8
Hence, the new price after the increase is $2.8 .
To know more about percent increase here:
https://brainly.com/question/13533684
#SPJ2
x3+y3+z3=k What does this equation mean please?
Answer:
Sum of cubes problem
Step-by-step explanation:
The equation x3+y3+z3=k is sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a "Diophantine equation" a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.
Answer:
it means x to the third power, plus y to the third power, plus z to the third power, equals some number (k).
Step-by-step explanation:
Dr. Smith purchased a used car for $11,325. Her state charges 8% tax for the car, $53 for license plates, and $40 for a state safety and emissions inspection. How much does she need to pay for these extra charges, not including the price of the car?
Answer:
999
Step-by-step explanation:
Answer:
999
Step-by-step explanation:
8% of 11,325 is 906
53 plus 40 is 93
906 plus 93 is 999
Can someone pls help me pls!
Answer:
refer to the picture attached for steps
Indices Home Learning
Simplify the following, leaving your answers in index notation.
1. (39)
2. Zf x 9f
38
3. 124 x 1210
4. (6m)
5. 252-3
6. 42g? = 7g?
7. 39 x 36
35
8. 116 x 116
112 x 11
Solve the following.
9. 7-2
10. 3-3
Answer:
We know that,
[tex](a^{x}) ^{y} =a^{xy}[/tex]
[tex]a^{x} *a^{y} =a^{x+y}[/tex]
[tex]\frac{a^{x} }{a^{y} } =a^{x-y}[/tex]
Let's solve now.
1) [tex](3^{8})^{4} =3^{32}[/tex]
2) [tex]7f^{3} * 9f^{9} =63f^{12}[/tex]
3) [tex]12^{4} *12^{10} =12^{14}[/tex]
4) [tex](6m^{5} )^{3} =6m^{15}[/tex]
5) [tex]\frac{2^{5} }{2^{-3} } =2^{8}[/tex]
6) [tex]\frac{42g^{7} }{7g^{2} } =6g^{5}[/tex]
7) [tex]\frac{3^{9}*3^{6} }{3^{5} } =\frac{3^{15} }{3^{5} } =3^{10}[/tex]
8) [tex]\frac{11^{6}*11^6 }{11^2*11^3} =\frac{11^{12}}{11^5} =11^7[/tex]
9) [tex]7^{-2} =\frac{1}{7^2} =\frac{1}{49}[/tex]
10) [tex]3^{-3} =\frac{1}{3^3} =\frac{1}{27}[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Write 49 as a product of primes
Answer:
7×7 = 49
Step-by-step explanation:
7 is a prime number. 7×7= 49 (product of primes)
PLS HELP!!
IM GIVING BRAINLIEST!!!
No stealing points, no links, only correct answers!!!!!
A
Plz help!!!!!! !!!!!!!!!!!
Answer:
R is at the ordered pair (4, -2)
Step-by-step explanation:
Help ASAP please i will mark brainliest who finishes first
pls be nice and neat
dont send links you CAN send photos of your answers
but i prefer typing your answers down thank you so much
Answer:
1-a) 78+x+16+x+24=180°
118+2x=180
2x=62
so x=31
Step-by-step explanation:
thats a
Answer:
1a) x = 31
1b) x = 12
2) angle A = 60 degrees
3) x = 40 degrees
Step-by-step explanation: