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
b) Solve x + 5x + 6 = 0
Answer:
Step-by-step explanation:
The solutions are
x=2,x=3
Explanation:
x2−5x+6=0
Here we can first factorise the expression and then find the solution:
Factorising by splitting middle term
x2−2x−3x+6=0x(x−2)−3(x−2)=0(x−2)(x−3)=0
Equating the two factors with zero to obtain solutions:
x−2=0,x=2x−3=0,x=3
Answer:
x + 5x + 6
x + 3x + 2x +6
x(1 + 3) + 2(x + 3)
(x + 3) (x+2) = 0
x = -3 (or) x = -2
One baseball team played 20 games throughout their entire season. If this baseball team
won 14 of those games, then what percentage of their games did they win? Round your
answer to the nearest whole number if necessary.
Answer:
70%
Step-by-step explanation:
The fraction of the game won is 14/20
Percent means out of 100
14/20 * 5/5 = 70/100
The percent is 70%
Will mark brainliest :)
Answer:
D
Step-by-step explanation:
The equation of the parabola is of the form
y = ax² + c ( where c is the y- intercept )
Here c < 0
Since the parabola has a maximum value and opens down then a < 0
Thus the only equation that could represent this parabola is
y = - x² - 3 → D
Ann and tom want to establish a fund for their grandson's college education. What lump sum deposit at a 12.7% annual interest rate compounded annually interest rate in order to have 20,000 in the fund at the end of 15 years
Answer:
2,683.34
Step-by-step explanation:
A=p(1+r/n)^nt
P=A/(1+r/n)^nt
A=20,000
r=12.7%=0.127
t=15
n=12
P=?
P=20,000/(1+/0.127/12)^12.7*15
=20,000/(1+0.0106)^190.5
=20,000/(1.0106)^190.5
=20,000/7.4534
P=2,683.3391
Approximately
P=2,683.34
What is the volume of the box pictured below?
A rectangular prism of length 1 and 1 over 8 m, width 4 over 5 m, and height 5 over 6 m is shown.
fraction 2 over 3 cubic meter
fraction 3 over 4 cubic meter
fraction 9 over 10 cubic meter
fraction 15 over 16 cubic meter
Answer:
3/4 cubic meter
Step-by-step explanation:
1 1/8 x 4/5 x 5/6= 3/4
If you have the following ordered pairs: (3,4) and (0,-2) Write an equation to represent them.
A) y=30 x -2
B) y=-2x +2
C) y=3x -2
D) y=2x+ -2
A little brown bat has eaten 1400 mosquitoes. It can eat 900 mosquitoes per hour. Let x be the number of hours it needs to hunt and eat 4100 mosquitoes.
Which equation could be used to solve for the number of hours?
can someone please help me put this in order
Answer:
camera D : 0.00087 ∠camera B : 0.00098∠camera C : 0.0011∠camera A : 0.0012
Step-by-step explanation:
if you rewrite in standard notation
camera A : 0.0012
camera B : 0.00098
camera C : 0.0011
camera D : 0.00087
Mattie is making a collar for her dog. She needs to buy some chain, clasp, and a name tag. She wants the chain to be 40 cm long. On meter of chain costs $9.75. The clasp is $1.29 and the name tag is $3.43. How much will it cost to make the collar? Estimate to check if your answer is reasonable.
Answer: $8.62
Step-by-step explanation:
Mattie wants to make a collar for her dog. She needs to buy some chain, clasp, and a name tag. Mattie wants the chain to be 40 cm long. On meter of chain costs $9.75, the clasp is $1.29 and name tag is $3.43.
Since 100 centimeters = 1 metre. Mattie needs 40cm and 1 meter of chain costs $9.75, cost of the chain Mattie needs will be:
= 40/100 × 9.75
= 2/5 × 9.75
= $3.90
Chain(40cm) = $3.90
Clasp = $1.29
Name tag = $3.43.
Cost to make collar will be:
= $3.90 + $1.29 + $3.43
= $8.62
Lucas made the list of all his assets and liabilities below. Highlight each item in
the box that is an asset.
.
• credit card balance: $2,576
checking account balance: $98.00
outstanding car balance: $12,500
• value of car: $22,800
jewelry: $1,750
student loan balance: $22,300
Based on the list above, what is Lucas's net worth?
Answer:
I got 12,148. Is that an option?
Step-by-step explanation:
98.00 checking account
car (value - outstanding balance) 12,500
plus jewelry $1750
If you square a googol, how many zeros will the answer have? Show your reasoning.
Answer:
200 zeros
Step-by-step explanation:
1 googol is the number 1 followed by a hundred zeros, right? Right. Using 'Laws of Indices', for instance, 10^2=100, ie 10×10=100. The number of zeros will always be the sum of the number of zeros of the multiplier and multiplicand. More example, 100×100=10000. So, I think it's reasonable to say that 1 googol×1 googol= the number one followed by two hundred zeros ♀️
Please help!! Someone said it was d.... and I think it’s either b or c..... now I am very confused :( giving 12-15 points!!
(Attached are pics of the question and answer choices)
Answer:
The answer is B, i hope this helped!
2/3 (m + 4) = 1/5 (3m+9)
[tex]\frac{2}{3} (m+4) = \frac{1}{5} (3m+9)[/tex]
[tex]\frac{2m+8}{3} = \frac{3m+9}{5}[/tex]
10m + 40 = 9m + 27
10m - 9m = 27 - 40
m = -13
Answer:
m = - 13
Step-by-step explanation:
2/3 (m + 4) = 1/5 (3m+9)
2/3m + 8/3 = 3/5m + 9/5
2/3m - 3/5m = 9/5 - 8/3
10/15m - 9/15m = 27/15 - 40/15
1/15m = - 13/15
m = - 13/15 / 1/15
m = - 13/15 * 15
m = - 195/15
m = - 13
How many times larger is the volume of a cylinder if the height is doubled?
Answer:
times 4
Step-by-step explanation:
Find the point-slope equation of the line using the point (1,2) and the slope of 3/2
Point slope form: y - y1 = m(x - x1)
(x1, y1) = a point
m = slope
We are given:
(x1, y1) = (1, 2)
m = 3/2
Put into the original equation:
y - 2 = 3/2(x - 1)
Best of Luck!
Victor wants to earn high interest and keep his money in an account for a while. Which of these is most likely the best option for Victor? A a savings account B a checking account C no bank account D a check casher
Answer:
Option A
Step-by-step explanation:
Many banks offer a rate of interest when putting your money into a savings account. The interest will help grow your money over time. Make sure you 're shopping around and check what fees are involved-you don't want to wind up paying more fees than you get in interest.
Ishmael jobs around a track that is in the shape of a regular pentagon. One side of the pentagon is 1/4 of a mile long. How far does Ishmael jog if he completes 6 laps around the track?
Answer:
He would’ve ran 7 1/2 miles
what is x in x + 4 = -x - 4
Answer: -4
Step-by-step explanation:
Answer:
x = - 4
Step-by-step explanation:
x + 4 = - x - 4
x + x = - 4 - 4
2x = - 8
x = - 8/2
x = - 4
please help answer both questions
Answer:
1. $503.08
2. 5071
Step-by-step explanation:
1. Perimeter = (pi × r) + d
= (3.14 × 27/2) + 27
= 69.39
Cost: 69.39 × 7.25 = $503.0775
2. 17 × (pi × d)
17 × 3.14 × 95
5071.1 feet
Step-by-step explanation:
Step 1: Answer the first question
Find the perimeter: [tex]P = (\pi *r)+d[/tex] But... let π be 3.14
[tex]P = (3.14 * \frac{27}{2}) + 27[/tex]
[tex]P = 42.39 + 27[/tex]
[tex]P = 69.39[/tex]
Find the price: $7.25 per foot
[tex]7.25 * 69.39[/tex]
[tex]\[/tex][tex]503.0775[/tex]
Answer: [tex]\[/tex][tex]503.0775[/tex]
Step 2: Answer the second question
Find the amount traveled: [tex]P = revolutions*\pi *d[/tex] But... let π be 3.14
[tex]P = 17 * 3.14 * 95[/tex]
[tex]P = 53.38 * 95[/tex]
[tex]P = 5071.1[/tex]
Answer: 5071.1 feet
Find x in this 45°-45°-90° triangle.
x=
Answer:
33
Step-by-step explanation:
because a triangle measure 90 degrees so you just subtract the amount that you add and got
Answer: 11 square root of 2
Find the area of the shaded region. Round your answer to the nearest tenth. Put the units on the answer for full credit
Answer:
Area of Shaded Region: 189 square centimeters
Step-by-step explanation:
~ To find the area of the shaded region, let us calculate the area of the rectangle added to the area of the two triangles, or the area of the whole triangle created from the two smaller triangles ~
1. Given dimensions of 15 by 9 centimeters, the area of the rectangle would be ⇒ 15 cm * 9 cm = 135 cm^2
2. It would be simpler if we were to consider the area of the larger triangle. The height in this case, by the Partition Postulate, would be 27 cm - 15 cm ⇒ 12 centimeters. Now provided that the shape with dimensions 15 cm by 9 cm is a rectangle, opposite sides are ≅, and thus ⇒ the base of this large triangle is 9 cm. That being said we can calculate the area of the triangle by ⇒ 1/2 * base * altitude ⇒ 1/2 * 9 cm * 12 cm ⇒ 6 cm * 9 cm ⇒ 54 cm^2
3. The area of the shaded region is thus 135 cm^2 + 54 cm^2 ⇒ 189 cm^2
Area of Shaded Region: 189 square centimeters
pls help me w this — show work work
Answer: 17.2
Step-by-step explanation:
You must use the law of sines, which says that sinA/a = sinB/b = sinC/c, where the side is the side across from the angle.
the length of side a = 16m, and the angle A = 25.
the length of side b = x, and the angle B = 27
1. sinA/a = sinB/b
2. sin25/16 = sin27/x
3. x(sin25)/16 = sin27
4. x = 16sin27/sin25
5. x = 17.2
1. How do you determine the constant that you should add to an expression in the form x^2+bx so that it becomes a perfect square trinomial?
2. When solving a quadratic equation by completing the square, why must you add the number that completes the square to both sides of the equation?
3. Why might you discard a negative solution in a real-world problem?
now heres a step by step explanation Step-by-step explanation: your welcome
The Service Club is choosing members at random to attend conferences in Sheboygan, Madison, La Crosse, and Green Bay. There are 15 members in the club, how many ways can they choose someone to go to the Sheboygan conference, someone different for the Madison conference, someone else for La Crosse, and one last person for Green Bay? SHOW YOUR WORK.
Answer:
There are 32760 ways to pick the members
Step-by-step explanation:
For the first place you have 15 possibilities, since every member of the club is available. For Madison you will have only 14, since you cant pick the same member than the one you picked for Sheyoygan. For the same argument, you will have 13 possibilities available for La Crosse, and only 12 for Green Bay.
We have to pick a combination using the possibilities that we have, thus, you have to multiply all 4 possibilities toguether to find the amount of ways to choose members to attend the conferences. This means that you will have a total of 15*14*13*12 = 32760 possibilities in total.
PLEASE HELP!!!
What is the solution to the inequality Three-fifths + y greater-than-or-equal-to StartFraction 11 over 15 EndFraction?
y greater-than-or-equal-to StartFraction 2 over 15 EndFraction
y greater-than-or-equal-to StartFraction 8 over 15 EndFraction
y greater-than-or-equal-to 1 and one-third
y less-than-or-equal-to 1 and one-third
Answer:
it is A
Step-by-step explanation:
i had the question on ed
Answer:
y greater - than - or - equal - to StartFraction 2 over 15 EndFraction
Step-by-step explanation:
What is the slope intercept for please help!
Answer:
y = -1/3 - 6
Step-by-step explanation:
its easy
The point (−6, a ) is on the line 3x − 5 y = 56 . Find a.
Answer:
(−6, a )
3x − 5 y = 56
3(-6) -- 5(a) = 56
--16 -- 5a = 56
--16 + 16 -- 5a = 56 + 16
--5a = 72
-5a / -5 = 72/-5
a = -14.4
Step-by-step explanation:
4.96X 10^6 = (x) (2x + 0.570)^2
Answer: no solution
Step-by-step explanation:
Answer: x = -1113.83787 ; x = 1113.26787
Step-by-step explanation:
Find the unit rate:
Sandra picked 55 oranges in 5 minutes.
How many did she pick in one minute?
Answer:
11
Step-by-step explanation:
55/5=11
Solve the equation k/1.5=3
Answer:
4.5
:):)
:):)
:):)