Answer:
y = 2(x + 4)² - 6
General Formulas and Concepts:
Order of Operations: BPEMDASCompleting the SquareStep-by-step explanation:
Step 1: Define function
y = 2x² + 16x + 26
Step 2: Find vertex form
Factor GCF: y = 2(x² + 8x + 13)Complete the Square: y = 2(x² + 8x + 4² + 13 - 16)Simplify: y = 2((x + 4)² + 13 - 16)Combine like terms: y = 2((x + 4)² - 6)Simplify: y = 2(x + 4)² - 65. An airplane 30,000 feet above the ground begins to descend at a
rate of 2,000 feet per minute. Choose an equation to model this
situation.
A y = 30,000 – 2,000x
B
y = 30,000x - 2,000
Cy= 30,000 + 2,000x
D y = 30,000x + 2,000
Answer:
A
Step-by-step explanation:
If the airplane is 30,000 feet above the air and descends 2,000 feet it's going down 2,000 feet per minute and cause we don't know how many minutes he was going down we put that as x. and multiply 2,000 for what ever x is.
Your Monthly Net Pay
If your gross monthly income will be $3,750, you need
to determine the net pay for your monthly budget.
Your monthly net pay is
Monthly gross pay
$3,750
Federal withholding
$238.00
Social Security
$232.50
Medicare
$54.38
State tax
$236.00
Net pay
$?
Answer:
2989.12
Step-by-step explanation:
238.00+232.50+54.88+236.00= 760.88
3750-760.88=2989.12
Express 27 1/3 in simplest radical form
Answer:
this answer is attached to the picture
Radical function or values are values inside the square root. This shows that the cube root of the given value is 3
Radical functionRadical function or values are values inside the square root. For instance;
√a is a radical function.
According to the law of indices
a^1/3 = ∛a
Given the expression
27^1/3 = ∛27
∛27 = 3
This shows that the cube root of the given value is 3
Learn more on radical function here:https://brainly.com/question/13430746
4. Find the length of side EG.
Answer:
42 cm
Step-by-step explanation:
the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)
so to find out line EG, you times 6 cm by 7. which is 42
In the problem 8^3 - 10 × 5 - 4
Answer: 458
Simplify
8³=8×8×8
Multiply
8×8×8=512
10×5=50
Subtract
512-50=462
462-4=458
Answer:
458
Step-by-step explanation:
8×8×8=512
10×5=50
512- 50 = 462
462-4= 458
Yuson must complete 30 hours of community service. She does 2 hours each day. Which linear equation represents the hours Yuson has left after x days?
A.) y= -2x + 30
B.) y= 2x + 30
C.) y= -2x - 30
D.) y= 2x - 30
Answer:
A
Step-by-step explanation:
Because it's subtracting 2 hours every day, the slope is -2. Also because it's 30 hours, it's 30. Therefore: A.) y=-2x+30 is the answer.
Hopes this Helps!
Tammy bought two rolls of tape. The first roll had 4.8 feet of tape and the second roll had 9.87 feet of tape. How many feet of tape did Tammy buy in all? *
Answer:
14.67ft of tape
Step-by-step explanation:
4.8+9.87=14.67
What is the solution to the linear equation? 2/4x - 1/2 = 1/3 + 5/6x
Answer:
x=-60/24 or -5/2
Step-by-step explanation:
u have to find X
2/4x - 1/2 = 1/3 + 5/6x
subtract 2/4x from both sides
to do that u need to have common denominator
2/4= 6/12
5/6=10/12
-1/2=1/3+4/12x
subtract 1/3 on both sides and u need common denominator
-1/2=-3/6
1/3=2/6
-5/6=4/12x
multiply 12/4 on both sides
x=-60/24
Answer:
x=-5/2
Step-by-step explanation:
2/4x-1/2=1/3+5/6x
-5/6x -5/6x
2/4x-5/6x-1/2 =1/3
+1/2 +1/2
6/12x-10/12x=2/6+3/6
-4/12x=5/6
x=5/6:(-4/12)=5/6*(-12/4)=-5/2
x=-5/2
Divide X^4 + 2x^2+1 by x+1
=x^5+2x^3+1+x÷×
Step-by-step explanation:
x^4+2x^2+(1÷x)+1
make 1÷x a fraction
x^4+2x^2+1/x+1
=x5+2x^3+1+x/x
I just started learning about rate and I am stuck on a question.(A watch keeps perfect time but only has an hour hand. If the hour hand is three fifths of the distance between 1and2, determine the actual time in hours and minutes)
Answer:
36 minutes past 1, or 1:36
Step-by-step explanation:
A watch normally has an hour hand that does one revolution in 12 hours.
It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.
Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.
The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.
3/5 of 60 minutes =
= 3/5 * 60 minutes
= 3/5 * 60/1 minutes
= 180/5 minutes
= 36 minutes
The time is 36 minutes past 1, or 1:36
Fill in the missing portions of the function to rewrite g(x) = 3a^2 − 42a + 135 to reveal the zeros of the function. What are the zeros of g(x)? (show your work!)
Enter your answers in the blanks:
g(x) = 3(_____)(_____)
Zeros: ______ and ______
Answer:
g(x) = 3(x-9)(x-5)
Zeros: x = 9 and x = 5.
Step-by-step explanation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]g(x) = 3x^{2} - 42a + 135[/tex]
So
[tex]a = 3, b = -42, c = 135[/tex]
[tex]\bigtriangleup = (-42)^{2} - 4*3*135 = 144[/tex]
[tex]x_{1} = \frac{-(-42) + \sqrt{144}}{2*3} = 9[/tex]
[tex]x_{2} = \frac{-(42) - \sqrt{144}}{2*3} = 5[/tex]
So
g(x) = 3(x-9)(x-5)
Zeros: x = 9 and x = 5.
a section in a stadium has 24 seats in the first row, 29seats in the second row. increasing by 5 seats each row for a total of 34 rows. how many seats are in this section of the stadium
Answer:
The answer is 2,142.
Step-by-step explanation:
Mark me brialianist of its right
factorise x square - 7 x minus 42
Answer:
x =(7-√217)/2=-3.865
x =(7+√217)/2=10.865 mark brainliest please
Step-by-step explanation:
Factoring x2-7x-42
The first term is, x2 its coefficient is 1 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -42
Step-1 : Multiply the coefficient of the first term by the constant 1 • -42 = -42
Step-2 : Find two factors of -42 whose sum equals the coefficient of the middle term, which is -7 .
-42 + 1 = -41
-21 + 2 = -19
-14 + 3 = -11
-7 + 6 = -1
-6 + 7 = 1
-3 + 14 = 11
-2 + 21 = 19
-1 + 42 = 41
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step 1 :
x2 - 7x - 42 = 0
Step 2 :
Parabola, Finding the Vertex :
2.1 Find the Vertex of y = x2-7x-42
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.5000
Plugging into the parabola formula 3.5000 for x we can calculate the y -coordinate :
y = 1.0 * 3.50 * 3.50 - 7.0 * 3.50 - 42.0
or y = -54.250
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-7x-42
Axis of Symmetry (dashed) {x}={ 3.50}
Vertex at {x,y} = { 3.50,-54.25}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-3.87, 0.00}
Root 2 at {x,y} = {10.87, 0.00}
Solve Quadratic Equation by Completing The Square
2.2 Solving x2-7x-42 = 0 by Completing The Square .
Add 42 to both side of the equation :
x2-7x = 42
Now the clever bit: Take the coefficient of x , which is 7 , divide by two, giving 7/2 , and finally square it giving 49/4
Add 49/4 to both sides of the equation :
On the right hand side we have :
42 + 49/4 or, (42/1)+(49/4)
The common denominator of the two fractions is 4 Adding (168/4)+(49/4) gives 217/4
So adding to both sides we finally get :
x2-7x+(49/4) = 217/4
Adding 49/4 has completed the left hand side into a perfect square :
x2-7x+(49/4) =
(x-(7/2)) • (x-(7/2)) =
(x-(7/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-7x+(49/4) = 217/4 and
x2-7x+(49/4) = (x-(7/2))2
then, according to the law of transitivity,
(x-(7/2))2 = 217/4
We'll refer to this Equation as Eq. #2.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(7/2))2 is
(x-(7/2))2/2 =
(x-(7/2))1 =
x-(7/2)
Now, applying the Square Root Principle to Eq. #2.2.1 we get:
x-(7/2) = √ 217/4
Add 7/2 to both sides to obtain:
x = 7/2 + √ 217/4
Since a square root has two values, one positive and the other negative
x2 - 7x - 42 = 0
has two solutions:
x = 7/2 + √ 217/4
or
x = 7/2 - √ 217/4
Note that √ 217/4 can be written as
√ 217 / √ 4 which is √ 217 / 2
Solve Quadratic Equation using the Quadratic Formula
2.3 Solving x2-7x-42 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -7
C = -42
Accordingly, B2 - 4AC =
49 - (-168) =
217
Applying the quadratic formula :
7 ± √ 217
x = —————
2
√ 217 , rounded to 4 decimal digits, is 14.7309
So now we are looking at:
x = ( 7 ± 14.731 ) / 2
Two real solutions:
x =(7+√217)/2=10.865
or:
x =(7-√217)/2=-3.865
Answer:
x^2 - 7x - 42
x^2 - x (21 - 14 ) - 42
x^2 - 21x + 14x -42
7x ( x - 3) + 14 ( x- 3)
(x -3) (7x + 14)
hope this helps you
Please help! Correct answer only!
I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking a 3 and then picking a 3?
Simplify your answer and write it as a fraction or whole number.
Answer:
You have three card : 3, 4, 5 and 6.
You first pick one card randomly, the probability of picking a 3 is:
P = 1/4
You then pick a second card without putting the first card back, the probability of picking a 3 is:
P = 1/3
=> The probability of picking a 3 and then picking a 3:
P = (1/4) x (1/3) = 1/12
Hope this helps!
:)
a)Work out an estimate for the mean time it took the students.Round your answer to 2 significant figures.
b)What fraction of the students finished in less than 20 minutes?
Find 3 rational numbers between ¼ and ½
Answer:
5/16 and 3/8 are two
Step-by-step explanation:
idk a third
3 1/2 divided by 2 3/5
Step-by-step explanation:
31/2×5/23 (use reciprocal)
31×5=155
155÷46=3.369565217
155/46
3 and 17/46
help i will give brainliest
Answer:
1/9
Step-by-step explanation:
The area of a polygon is the old area multiplied by the scale factor squared
New area = old area ( SF) ^2
The scale factor is 1/3
(1/3) ^2 = 1/9
The fraction is 1/9
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for . For cylinder A , h=5 m &c=3 m, cylinder B, h=3 m & c=5 m.
Answer:
Cylinder B has a greater volume
Step-by-step explanation:
Volume of a cylinder[tex]=\pi r^2h[/tex]
Cylinder A
h=5m, r=3m
Volume
[tex]=3.14 *3^2*5\\=141.3m^3[/tex]
Cylinder B
h=3m, r=5m
Volume
[tex]=3.14 *5^2*3\\=235.5m^3[/tex]
Cylinder B has a greater volume.
When Mr. Shelton preheated his oven, the oven's temperature rose 3 degrees in 1/6
of a minute. At that rate, how much will the oven heat up in 1 minute?
Answer:
Step-by-step explanation:
18 degrees
It’s a proof... but I don’t think it’s that hard! *sorry I’m just dumb so please do this proof for me...*
Answer:
1. given
2. bisected angles create two congruent angles
3. same side length
4. ASA: angle, side, angle congruency
5. the two triangles are congruent, meaning all of their side lengths correspond, meaning that YZ and WZ are equivalent.
Use the Distributive Property to determine which of the following statements is equivalent to 5(6 – 1).
A. 6 - 1
B. 5 • 5
C. 30 - 5
D. 11 - 5
[tex]\text{You would use the distributive property to get your answer} \\\\\text{This means that you would distribute the 5 to the numbers inside the}\\\text{parenthesis}\\\\\text{When you distribute, you would multiply}\\\\\text{Distribute:}\\\\5(6-1)\\\\5(6)-5(1)\\\\30-5\\\\\text{You would see that this is equal to answer choice C, therefore making}\\\text{C your answer}\\\\\boxed{\text{C). 30 - 5}}[/tex]
Correct answers only please! I keep loosing points...
Quincy has $6,000 in a savings account that earns 4% interest, compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$ 7,299.92
Step-by-step explanation:
A = $ 7,299.92
A = P + I where
P (principal) = $ 6,000.00
I (interest) = $ 1,299.92
Which of the following is always true of the vertical angles formed by
perpendicular lines? Check all that apply.
A. They are congruent.
B. They are right angles.
C. They are acute.
D. They are obtuse.
Answer:
A
Step-by-step explanation:
This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.
When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.
What is angle?The angle can be defined as the one line inclined over other line.
Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.
Thus, when two perpendiculars line intersect the angles formed must be a right angle.
Learn more about angles here:
https://brainly.com/question/13954458
#SPJ2
Some help please? I’m lost
Answer:
1/2
Step-by-step explanation:
When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!
Answer:
1/2.
Step-by-step explanation:
Sine = opposite side / hypotenuse.
The side opposite 60 degrees has length√3 and the hypotenuse = 2.
By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)
= 1 unit.
So cos 60 = adjacent / hypotenuse = 1/2.
A stock has a price of $72.31. This is $6.28 less than the price of the stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday. An equation is =72.31. The price of the stock yesterday was $ .
Answer: The price of the stock yesterday was $78.59
Step-by-step explanation:
p - 6.28=72.31
+6.28 + 6.28
p= 78.59
Answer:
78.59$
Step-by-step explanation:
p-6.28=72.31
p=72.31+6.28
p=78.59$
hey everyone! can u guys please help i really struggle in math and i just need some help
i will follow and mark u as brainleist even if u know a friend or google that could help me
thanks everyone and have a great corona time day
Answer:
d= 5.2
[][][]-[][][]
P = √5.2 ^3
P = √5.2 × 5.2 × 5.2
P = √140.608 (plug into calculator)
P = 11.857824421
P = 11.86
The orbital period of Jupiter is 11.86 Earth years.
Pleaseee helpp i will let you brainlest
Answer:
13
Step-by-step explanation:
use Pythagorean
it is usually, 5, 12, 13
In how many ways can a
recorder, facilitator, and
questioner be chosen in a club
containing 14 members?
Answer:
The answer is 364. There are 364 ways of choosing a recorder, a facilitator and a questioner froma club containing 14 members.
This is a Combination problem.
Combination is a branch of mathematics that deals with the problem relating to the number of iterations which allows one to select a sample of elements which we can term "r" from a collection or a group of distinct objects which we can name "n". The rules here are that replacements are not allowed and sample elements may be chosen in any order.
Step-by-step explanation:
Step I
The formula is given as
[tex]C (n,r) = \frac{n}{r} = \frac{n!}{(r!(n-r)!)}[/tex]
n (objects) = 14
r (sample) = 3
Step 2 - Insert Figures
C (14, 3) = [tex](\frac{14}{3})[/tex] = [tex]\frac{14!}{(3!(14-3)!)}[/tex]
= [tex]\frac{87178291200}{(6 X 39916800)}[/tex]
= [tex]\frac{87178291200}{239500800}[/tex]
= 364
Step 3
The total number of ways a recorder, a facilitator and a questioner can be chosen in a club containing 14 members therefore is 364.
Cheers!
Please find attached.
Answer:
5.83
Step-by-step explanation:
[tex]c=\sqrt{a^2+b^2\\} =\sqrt{3^2+5^2}\\=5.83[/tex]
Answer:
5.83
Step-by-step explanation:
rs²=3²+5²
rs²=9+25
rs²=34
rs=5.83