Answers
Answer:
a) x = 1, x = -7
b) (-3, -48)
c) x = -3
d) upwards
Step-by-step explanation:
Given quadratic equation:
[tex]y=3(x-1)(x+7)[/tex]
Part (a)Intercept form of a quadratic equation:
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-interceptsa is some constantComparing the formula with the given equation:
⇒ p = 1
⇒ q = -7
Therefore, the x-intercepts of the given equation are x = 1 and x = -7.
Part (b)The midpoint between the two x-intercepts is the x-coordinate of the vertex.
[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]
Therefore, the x coordinate of the vertex is -3.
To find the y-coordinate of the vertex, substitute this into the given equation:
[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]
Therefore, the coordinates of the vertex are (-3, -48).
Part (c)The x-coordinate of the vertex is the axis of symmetry.
Therefore, the axis of symmetry is x = -3.
Part (d)If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.
If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.
From inspection of the given equation, the leading coefficient is 3.
Therefore, the parabola opens upwards.
Learn more about quadratic equations here:
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Related Questions
3x+9=36
Show your steps
Answers
Answer:
x=9
Step-by-step explanation:
3x+9=36
subtract 9 from both sides
3x=27
divide by 3 on both sides
x=9
The solution to the equation 3x + 9 = 36 is x = 9.
To solve the equation 3x + 9 = 36, we'll perform the necessary steps to isolate the variable x on one side of the equation.
Given equation:
3x + 9 = 36
First, we'll subtract 9 from both sides to eliminate the +9 term on the left side:
3x + 9 - 9 = 36 - 9
3x = 27
Next, to isolate the variable x, we divide both sides by 3:
(3x)/3 = 27/3
x = 9
Therefore, the solution to the equation 3x + 9 = 36 is x = 9.
In this equation, we start with an expression involving the variable x and a constant term. By performing algebraic operations, we manipulate the equation to have x on one side and the constant value on the other side. This isolates the variable and provides us with a specific value for x that satisfies the equation. In this case, the value of x is determined to be 9, which can be verified by substituting it back into the original equation to see if it holds true.
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Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement. The polynomial simplifies to an expression that is a with a degree of .
Answers
Answer:
The answer is below
Step-by-step explanation:
Select the correct answer from each drop-down menu. Simplify the given polynomial and use it to complete the statement.
(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)
.The polynomial simplifies to an expression that is a____
A.quadratic
B.liner
C.constany
A.trinomial
B.binomial
C.monomial
with a degree of____
A.1
B.2
C.0
Solution:
A polynomial is an expression involving operations of addition, subtraction, multiplication, exponents which consists of variables and their coefficient. A trinomial is a polynomial consisting of three terms, while a binomial consist of two terms and a monomial consist of one term.
The degree of a polynomial is the highest degree of any of the terms of the polynomial. If it has a degree of 0 it is a constant, a degree of 1 it is linear while for a degree of 2 it is quadratic.
(-5x² - 2x + 4) + (8x² - x - 1) + (x + 2)(x - 5)
= (-5x² - 2x + 4) + (8x² - x - 1) + (x² -5x + 2x - 10)
= (-5x² - 2x + 4) + (8x² - x - 1) + (x² - 3x - 10)
= (-5x² + 8x² + x² - 2x - x - 3x + 4 - 1 - 10)
= 4x² - 6x - 7
Therefore:
.The polynomial simplifies to an expression that is a quadratic trinomial of degree 2.
A pair of shoes are on sale, they are marked 40% off. The discount is equal to 20 dollars, what is the original price of the shoes
Answers
Answer:
$44
Step-by-step explanation:
What is an
equation of the line that passes through the points (4,-4) and
(-6,-4)? PLEASE I HAVE TO AWNSER IN 5 minutes
Answers
Step-by-step explanation:
[tex]y = - 4[/tex]
[tex]y = - 4[/tex]
Answer:
y=-4
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-4-(-4))/(-6-4)=(-4+4)/-10=0/-10=0
slope is 0
y-y1=m(x-x1) where m=slope
y-(-4)=0(x-4)
y+4=0
y=0-4=-4
y=-4
answer my question PLEASE
Answers
Answer:
130
Step-by-step explanation:
1/4t-6=-4
What does t equal?
Answers
Answer:
t = 8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
1/4t - 6 = -4
Step 2: Solve for t
[Addition Property of Equality] Add 6 on both sides: 1/4t = 2[Division Property of Equality] Divide 1/4 on both sides: t = 8Answer:
t=8
Step-by-step explanation:
1/4 = 0.25
0.25t - 6 = -4
0.25t = -4 + 6
0.25t = 2
t = 2/0.25
t = 8
A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 .
Answers
Answer:
3.24 feet
Step-by-step explanation:
A 17 -ft ladder leans against a building so that the angle between the ground and the ladder is 79 . Find the distance between the building and the ladder
We solve the above question using the Trigonometric function of Cosine
cos x = Adjacent/Hypotenuse
Adjacent = x feet
Hypotenuse = 17 ft
The angle = 79°
Hence,
cos 79 = x/17
Cross Multiply
x = cos 79 × 17
x = 3.2437529214.feet
Approximately = 3.24 feet
Therefore, the distance between the ladder and the building = 3.24 feet
answer asap!!! PLS HELP.
what is the value of x in the figure??
a. 90
b. 60
c. 120
d. 30
Answers
Answer:
Step-by-step explanation:
the x is 30
60=2x
x=30
Answer:
d
Step-by-step explanation:
its d i think
Posts are 4 1/4 feet in length. Posts must be installed 7/8 feet below ground level, What will be the height of fence?
Answers
Answer:
Step-by-step explanation:
4 1/4x7/8
I think 119/32
The height of fence will be "[tex]\frac{41}{8}[/tex]".
According to the question,
Length of posts,
= [tex]4\frac{1}{4} \ feet[/tex]
Length of posts below ground level,
= [tex]\frac{7}{8} \ feet[/tex]
Now,
→ The height of the fence will be:
= [tex]4\frac{1}{4} +\frac{7}{8}[/tex]
= [tex]\frac{17}{4}+\frac{7}{8}[/tex]
= [tex]\frac{34}{8}+\frac{7}{8}[/tex]
= [tex]\frac{34+7}{8}[/tex]
= [tex]\frac{41}{8}[/tex]
Thus the above is the right answer.
Learn more:
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A: 5x²+3xy +2y B: 2y²-xy +4x²
С: 12xy+4x²-3y. then :- 1) А-В-С , 2) 2A+3B+4C 3)3A-4B--2C. pls help me will mark u as brainliest
Answers
Answer:
-3x² -2y² -8xy +5y
34x² + 51xy - 8y + 6y²
7x² - 11xy +12y - 8y²
Step-by-step explanation:
Given:
A: 5x²+3xy +2y
B: 2y²-xy +4x²
С: 12xy+4x²-3y
Find:
1) А-В-С
2) 2A+3B+4C
3) 3A-4B--2C
Computation:
1) А-В-С
5x²+3xy +2y - [2y²-xy +4x²] - [12xy+4x²-3y]
5x²+3xy +2y -2y² +xy -4x² -12xy -4x²+3y
-3x² -2y² -8xy +5y
2) 2A+3B+4C
2[5x²+3xy +2y]+3[2y²-xy +4x²]+4[12xy+4x²-3y]
10x² + 6xy + 4y + 6y² - 3xy + 8x² + 48xy + 16x² - 12y
34x² + 51xy - 8y + 6y²
3) 3A-4B-2C
3[5x²+3xy +2y]-4[2y²-xy +4x²]-2[12xy+4x²-3y]
15x² + 9xy + 6y -8y² + 4xy - 16x² - 24xy - 8x² +6y
7x² - 11xy +12y - 8y²
Can someone pls help me with this ?
Answers
Answer:
1,3,4,5
Step-by-step explanation:
I cant see 8
helpp PLSSS 20 PONITS!!
Answers
Answer:
c I think
Step-by-step explanation:
can you help me with this question In Lines 23 and 24 of his poem "Chicago", Sandburg uses which poetic device? A Simile - a comparison of two unlike things using "like" or "as" B. Metaphor - a comparison of two unlike objects C. Repetition
Answer: 20
Step-by-step explanation: I LOVE THIS I HATE THIS I CAN SEE THIS SO I JUST GEUSSED HOPE IT IS RIGHT BYE
PLEASE HELP ME I NEED TO TIRN THIS IN AND I DONT KNOW HOW TO DO THIS !
Answers
Answer:
what grade is this ?
Step-by-step explanation:
What is the area of the real bedroom?
Answers
Answer:
area of real bedroom = 32 cm²
hope it helps..
Answer:
Bedroom: 32 cm living room: 81 cm
Step-by-step explanation:
Bedroom: 4 x 8 = 32
Living room : 9 x 9 = 81
( if combining bedroom and living room, it’s 113 cm)(81 + 32 = 113)
Hope this helps
yayyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answers
Answer:
It b
Step-by-step explanation:
We know this because 1/2 is 0.5 while 2/3 is 0.67. With this we can say that 1/2 is least than 2/3
Hope this Helped
Helpppp!!!!
Which of the following are square roots of the number below? Check all that
apply.
49
A. 7
B. 28
C. 8
D. -491/2
E. -7
F. 491/2
Answers
Answer:
Step-by-step explanation:
Because 7(7)=(-7)(-7)=49 the square roots of 49 are 7 and -7
solve : 105/103 = _____
Answers
Answer:
1.02
Step-by-step explanation:
lütfen yardım edin acil lütfen
Answers
Answer:
cevap 480 dirrrrrrrrrrr
can someone help me plz
Answers
Answer:
Step-by-step explanation:
(2-4x)+(2-4x)+(-2x+8)=12-10x
(WILL GIVE BRAINLYIST IF ANSWER IS RIGHT!)
Choose all the expressions that is equal to 0.25(4y - 36)
1. Y - 9
2. -18/2 - y
3. 0.25y - 36
4. -1/2(-2y + 18)
Answers
Answer:
The answer is 1 and 4
Step-by-step explanation:
.25 x 4y = Y
36 divided by 4 = 9
Round 26,127 to the nearest hundred.
Answers
5 or more add 1
4 or less stays the same
2/7 of the person at a concert are children 1/4 and men and the rest women what fraction are women
Answers
Answer:
15/28 are women
Step-by-step explanation:
2/7 + 1/4 + x = 100%
2/7+1/4= 15/28
9514 1404 393
Answer:
13/28
Step-by-step explanation:
The fraction that are women is found by subtracting the given fractions from 1.
1 - 2/7 - 1/4 = 28/28 -8/28 -7/28 = (28 -8 -7)/28 = 13/28
The fraction that are women is 13/28.
Find the volume of the prism. cubic cm. 15cm 5cm 3cm
Answers
Answer:225cm
Step-by-step explanation:15x5x3
Answer:
The area is 225 ft. sq.
Step-by-step explanation:
Multiply 15cm, 5cm, and 3cm together!
pls help. 6th grade math.
Answers
Answer:
Note: If this is really sixth grade math, then im a cucumber. It's way easier than MY math, and I'm in 6th grade lol :P
Another Note: Please vote me "Brainliest", I put a lot of work into this :)
1. 40
2. 60
3. 1.35
4. 6
5. Do this yourself, it requires actually explaining and you have to use your own words. :)
6. Do this yourself, it requires actually explaining and you have to use your own words. :)
7. Do this yourself, it requires actually explaining and you have to use your own words. :)
8. 600 people
9. 4200 people
10. 149 people
11. Sahil came up with his answer so quickly because if 45 is 10% of x, then obviously 30% of x would be 45 times 3 and that is 135. Due to this, he quickly new that the number of people between the ages of 30 and 49 that voted is 135 people.
That's it, please heart my answer and vote me brainliest :)
Step-by-step explanation:
Do you really need this part? I didn't do it because it would take forever LOL
Neeeeeeeeed your help
Answers
Answer:
9/15=3/5
so 3/5 is equivalent fraction of the 9/15
x/5 = 2,2 help??????
Answers
Answer: 22
Step-by-step explanation:
Multiply: (2x − 5)(4x2 + 7x − 11)
Answers
Answer:
14x²-41x+15
Step-by-step explanation:
Answer:
8x^3-6x^2-57x+55
Tell me if you would like an explanation If you need one :D
Rodrigo plans to buy packs of baseball cards until he gets the card of his favorite player, but he only has enough money to buy at most three packs. Suppose that each pack has a 10 % 10%10, percent chance of containing the card Rodrigo is hoping for. The table below displays the probability distribution of X XX, the number of packs of cards Rodrigo buys. X = # of packs X=# of packsX, equals, \#, start text, space, o, f, space, p, a, c, k, s, end text 1 11 2 22 3 33 P ( X ) P(X)P, left parenthesis, X, right parenthesis 0.10 0.100, point, 10 0.09 0.090, point, 09 0.81 0.810, point, 81 Calculate the mean of X XX.
Answers
Answer: 2.71 packs
Step-by-step explanation:
A number is multiplied by 6, and the result is 48.6.
Answers
Answer:
8.1
Step-by-step explanation:
We denote the number as x.
6 * x = 48.6
We can divide both sides by 6 to get,
x = 8.1
Answer:
8.1
Step-by-step explanation:
Let the unknown number be n. Translating this statement into symbols, we get:
6n = 48.6
Solving for n by dividing both sides by 6, we get n = 8.1
The number is 8.1
what is nthe anwer
5 - 2x + 50
Answers
Step-by-step explanation:
= 55 - 2x is the answer .
plz mark my answer as brainlist if you find it useful.
Answer:
Add 5 and 50
−2x + 55
Step-by-step explanation: