The examples of error and trial method and quadratic system are shows below.
Number problems and try to solve either trial and error or a Quadratic System
Trial and error is a fundamental method of Problem solving. It is characterized by repeated, varied attempts which are continued until success, or until the agent stops trying. Until getting the right answer the problem is repeating through various steps. This type of problem solving is called trial and error method.
A linear quadratic system is a system containing one linear equation and one quadratic equation (which is generally one straight line and one parabola). A simple linear system contains two linear equations (which is two straight lines).
ERROR AND TRIAL METHOD
Question: 44 people live in eight houses (3 on each side of the Albert Square). Each house has a different number of people living in it. Each line of three houses has 15 people living in it. How many people live in each house?
Solution: Simplifying, we have to get 4 sets of numbers, each of which add up to 15. So start guessing.
The average number of people in a house is 44/8 is roughly 4.5. So what numbers should we take? 2, 3, 4, 5, 6, 7, 8, 9. Now, we should also have an average close to 5 for each set. Let's start:
Set 1: 3, 5, 7
Set 3: 2, 4, 9
Now, the other two sets will have an overlap. So let's guess the overlaps:
Set 2: Overlaps are 2 and 7. So the third number will be 6. Because we have not used 6 yet.
Set 4: Overlaps are 3 and 9. Then the third number ends up to 3 again. Wrong guess! So we need to try again. Overlaps are 3 and 4. In this case third number works out to be 8, which we have not used. So here is the answer
The first row: 2,6,7.
Second row: 4,8,3.
First column : 2,9,4.
Second column: 7,5,3.
QUADRATIC SYSTEM:
Find the points of intersection between the line y=2x+1 and the parabola y=x2−2.
Substitute 2x+1 for y in y=x2−2.
2x+1=x2−2
Write the quadratic equation in standard form.
2x+1−2x−1=x2−2−2x−10=x2−2x−3
Use the quadratic formula to find the roots of the quadratic equation.
Here, a=1, b=−2, and c=−3.
x=−(−2) ± (−2)2 − 4(1)(−3)√2(1)=2 ± 4 + 12√2=2 ± 42=3, −1
Substitute the x-values in the linear equation to find the corresponding y-values.
x=3⇒y=2(3)+1
=7x=−1⇒y=2(−1)+1 =−1
Therefore, the points of intersection are (3,7) and (−1,−1).
Graph the parabola and the straight line on a coordinate plane.
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Genesis wants to ride her bicycle 42.8 miles this week. She has already ridden 5
miles. If she rides for 6 more days, which tape diagram could be used to represent the
context if m represents the aaverage number of miles she would have to ride to meet
her goal?
m is the average number of miles which is 4.3 miles
Total miles Genesis travel in a week is 42.8 miles.
Here we have to find m which is the average number of miles she would travel.
She ride for 6 more days and had already traveled 5 miles.
From the above question, we have an equation
5 + 6m = 42.8
6m = 37.8
m = 6.3
Therefore m is 6.3 which is the average number of miles Genesis will ride to meet her goal.
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The integer 5 makes which of the following equations false?
A: 3m + 4 = 6m
B: −5(t − 7) = 10
C: 17 = 4x − 3
D: t + 9 = 14
Answer:
a) 3m + 4 = 6m is false.
Step-by-step explanation:
A) 3m + 4 = 6m
→ 3(6) + 4 = 6(5)
→ 18 + 4 = 30
→ [ 22 ≠ 30 ]
So, the equation is false.
B) -5(t - 7) = 10
→ -5(5 - 7) = 10
→ -5 × -2 = 10
→ [ 10 = 10 ]
So, the equation is true.
C) 17 = 4x - 3
→ 17 = 4(5) - 3
→ 17 = 20 - 3
→ [ 17 = 17 ]
So, the equation is true.
D) t + 9 = 14
→ 5 + 9 = 14
→ [ 14 = 14 ]
So, the equation is true.
2. Three times the sum of a number and 4 is 21
less than the number times 6. Find the number
Answer:
11
Step-by-step explanation:
Given two expressions involving the same unknown number, you want to find the number.
Setup3(x +4) . . . . three times the sum of a number and 4
6x -21 . . . . 21 less than the number times 6
These two expressions have the same value, so we can write the equation ...
3(x +4) = 6x -21
SolutionEliminating parentheses, we have ...
3x +12 = 6x -21
33 = 3x . . . . . . . . add 21-3x
11 = x . . . . . . . . . divide by 3
The number is 11.
A pre-paid cell phone company charges $19.5 as a monthly access fee and $0.16 per minute of calling time.
Express the monthly cost C in terms of minutes of call time.
What will the monthly cost be if you make 367 minutes of calls this month? $
The monthly cost C expressed in terms of minutes of call is: C=19.5+0.16x
The monthly cost if you make 367 minutes of call is $78.22
How the monthly cost modeled?
The monthly cost is modeled using the straight-line equation which comprises of the monthly access fee, which is the fixed charge and the variable charge per minute of $0.16
C=19.5+0.16x
x is the number of minutes of call time
monthly cost when x is 367 minutes
monthly cost=19.5+(0.16*367)
monthly cost=19.5+58.72
monthly cost=$78.22
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use the product rule to simplify the following expression
13
√x
We have been provided with this exponential equation y= 13√x + 13√[tex]x^{7}[/tex]
The product rule for solving the exponential powers is [tex]x^{n}[/tex] × [tex]x^{m}[/tex]= [tex]x^{n+m}[/tex]
, which means if the base is same and the variables are multiplied then the powers of the bases get added.
By using the product rule in the given exponential problem, it can be written as:
y = 13 √x ×√[tex]x^{7}[/tex]
y =13 √[tex]x^{1+7}[/tex]
y =13 √[tex]x^{8}[/tex]
Roots means the power of the base is half
y =13 [tex]x^{4}[/tex]
Correct question is Use the product rule to simplify the following expression
y= 13√x + 13√[tex]x^{7}[/tex]
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Graph the function f(x)=-x^ 2+2
Answer:
just plot it nicely
Step-by-step explanation:
hope this help
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
?
10 cm
6 cm
11 cm
5 cm
14 cm
Answer:
4 cm
Step-by-step explanation:
14 - 10 = 4
4cm
Step-by-step explanation:
10-14=4 hope it helps
Math help ten points and brainliest this is what I got first
Answer:
D. 2,500 square feet
Step-by-step explanation:
The scale of a map is 1:500 000.
The area of a lake on the map is 12cm".
Calculate the actual area of the lake in km?.
The scale of a map is 1:500 000. The actual area of the lake in km is 3x10¹² km².
What is meant by the scaling on the map?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult.
• If 1 centimeter on a map corresponds to 500 000 km on the earth, then 1 cm2 would be equivalent to 1 cm² = (500000km) 2
=25×10¹⁰ km²
• The lake's exact area may now be determined by multiplying 12 cm² by 25 × 10¹⁰ km² (3 × 10¹² km²)
As a result, the distance between the towns is 0.000344 cm on the map, while the lake's real area is 3x10¹² km².
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What is a scale factor
Answer:
Scale factor is a ratio between an object and a new object, which is said to be the same object but in a new size or form.
Tim earns $18 cleaning a home. How many homes did he clean, if he made 90 dollars?
Answer:
[tex]x = 5[/tex]
Step-by-step explanation:
From the given:
$18 ——→ 1 home
$90 ——→ x home
Cross multiply the above and make x the subject of formula.
[tex]18x = 90[/tex]
Now, divide both sides by 18 to find the value of x.
[tex] \frac{18x}{18} = \frac{90}{18} [/tex]
Therefore:
Tim made $90 from cleaning 5 homes.
In September 2016, the cost of gasoline in Berlin was around 1.29 euros per liter. What would the equivalent cost be in U.S. dollars per gallon? 1 U.S. dollar ≈ 0.896 euros 1 gallon ≈ 3.785 liters
Answer:
3.89
Step-by-step explanation:
Determine whether C_ ,C , both or neither can be replaced in the blank to make the statement true
Answer:
I don't understand what you're trying to ask?
Step-by-step explanation:
-7 ≤ g + 8 + 2g ≤ 2
Simplify
2
g
−
(
8
−
g
)
.
Tap for more steps...
3
g
−
8
=
7
g
−
10
Move all terms containing
g
to the left side of the equation.
Tap for more steps...
−
4
g
−
8
=
−
10
Move all terms not containing
g
to the right side of the equation.
Tap for more steps...
−
4
g
=
−
2
Divide each term in
−
4
g
=
−
2
by
−
4
and simplify.
Tap for more steps...
g
=
1
2
The result can be shown in multiple forms.
Exact Form:
g
=
1
2
Decimal Form:
g
=
0.5
Original: 26 ; new amount: 18
That means 8 has been subtracted from the original amount to get at the new one
Write the coordinates of the vertices after a reflection over the line x = -1.
The coordinates of the vertices after a reflection over the line x = -1 are
A’ = (-12, 3).
B' = (-1, -7)
C' = (-12, -6)
Given that the coordinates of the vertices after a reflection over the line
x = -1.
For reflection about a vertical axis (x = -1), we need only be concerned with the x-components of the vertices.
Given any point (x, y), the new x’ value would be the distance ‘d’ from the reflection axis (x -(-1)), then inverted for reflection about the axis of reflection x = -1… x’ = -1 -d… where d = (x - (-1)) = (x + 1)
x’ = -1 -(x + 1) = -x -2
Given a point from the graph as
A = (-10, -7), A’ = (-10-2 , -7) = (-12, 3).
B = (-1, -7), B’ = (-1, -7) = (-1, -7). (since on the same line.)
C = (-10, -6), C’ = (-10-2, -6) = (-12, -6).
This reflection works for vertices on either side of the reflection axis, such as if you have a triangle with some vertices on one side, and some on the other, straddling the axis.
The coordinates of the vertices after a reflection over the line x = -1 are
A’ = (-12, 3).
B' = (-1, -7)
C' = (-12, -6)
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Which is the midpoint of segment AB when A is at (5, 7) and B is at (3, 1)?
How would you sketch a plot of the line on -3x+5y=15? I got an answer with a fraction and I'm not sure if that's right
The equation y = 3/5x + 3 can be plotted to represent the graph of -3x + 5y = 15
How would you sketch a plot of the line on - 3x + 5y = 15 ?The equation of the plot is given as
-3x + 5y = 15
Divide through the equation of the plot by 5
So, we have
-3/5x + y = 3
Add 3/5x to both sides of the equation
So, we have
y = 3/5x + 3
The above means that the equation y = 3/5x + 3 can be plotted to represent the graph of -3x + 5y = 15
Hence, the equation y = 3/5x + 3 can be plotted to represent the graph of -3x + 5y = 15
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A couch and coffee table cost a total of 1212 . The cost of the couch is two times the cost of the coffee table. Find the cost of each item.
Answer:
x + 2x = 1161
3x = 1161
x = 1161/3 = 387
2x = 2(387) = 774
cost of coffee table: $387
cost of couch: $774
Step-by-step explanation:
The teeth on this key are busted.
Now they must be readjusted.
The code is CSHDG.
what is factorization?when you break a number down into smaller numbers that, multiplied together, give you that original number.
Given:
G: x² +2x -8 / 2x³ -24x² +64x
=(x+10)(x-8)/ 2x(x-4)(x-8)
=x+ 10/ 2x(x-4)
D: 6x³ + 42x²/2x² + 26x +84
=6x²(x+7)/2(x+7)(x+6)
=3x²/(x+6)
C: x³ -x²-42x/2x² -20x + 42
=x(x-7)(x+6)/(x-3)(x-7)
x(x+6)/(x-3)
S:2x² -10x +48 /8x+ 64
=2(x+8)(x-3)/8(x+8)
H: 3x² -39x + 90/ x²-3x-90
=3 (x-3)(x-10)/(x+7)(x-10)
=3(x-3)/(x+7)
Hence, the matching code is CSHDG.
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The complete question is attached below.
If the cost of 40 books is ₹ 360, how much will 30 books cost?
Answer:
270Step-by-step explanation:
If the cost of 40 books is ₹ 360, how much will 30 books cost?
we can solve with an equation
40 : 360 = 30 : x
x = 360 * 30 : 40
x = 270 £
or
we find the price of a book and multiply it by 30
360 : 40 * 30 =
9 * 30 =
270 £
James said that he would need 25 red beads to make 75 bracelets. Is he correct? How did he get that answer?
Answer:
He is wrong.
Step-by-step explanation:
Usually a bracelet has at least 5 beads, so with 25 beads the maximum is 5 bracelet.
Solve (x - 5)² = 3.
O A. x = 8 and x = −2
OB. x=5± √3
OC. x = 3+√5
O D. x=-5±√√3³
Answer:
B. x=5±√3
Step-by-step explanation:
Let's solve your equation step-by-step.
(x−5)²=3
Step 1: Simplify both sides of the equation.
x²−10x+25=3
Step 2: Subtract 3 from both sides.
x²−10x+25−3=3−3
x²−10x+22=0
For this equation: a=1, b=-10, c=22
1x²+−10x+22=0
Step 3: Use quadratic formula with a=1, b=-10, c=22.
x=−b±√b²−4ac/2a
x=−(−10)±√(−10)²−4(1)(22)/2(1)
x=10±√12/2
x=5+√3 or x=5−√3
A water park has pools, slides, and rides that, in total, make use of 6.9 × 105 gallons
of water. They plan to add a ride that would make use of an additional 85, 000
gallons of water. Use scientific notation to express the total gallons of water made use
of in the park after the new ride is installed.
Answer:
x10 gallons
Answer:
x10 gallons
Step-by-step explanation:
you said it
Calculate the product of given fractions. Write your answer in lowest terms.
3/4 X 9/15.
Answer:
[tex] \frac{9}{20} [/tex]
Step-by-step explanation:
[tex] \frac{3}{4} \times \frac{9}{15} [/tex]
The denominator 15 will be divided by the numerator 3 giving :
[tex] \frac{1}{4} \times \frac{9}{5} \\ = \frac{1 \times 9}{4 \times 5} [/tex]
Final answer:
[tex] \frac{9}{20} \: or \: 0.45[/tex]
What company has the absolute advantage when it comes to producing phones?
a. Gonzalez and Bros. Inc
b. The G company Inc
c. they both do
d. neither
(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.
Absolute advantage theory
Adam Smith, an economist from the 18th century, introduced the idea of absolute advantage in his book The Wealth of Nations to explain how nations might profit from trade by specializing in producing and exporting the things that they can manufacture more successfully than other nations.
On the other hand, low-cost manufactured items are produced and exported by China, Thailand, and Vietnam. These three nations enjoy a distinct advantage as a result of their significantly reduced unit labor costs.
Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.
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find the nth term of a sequence for 1,7.13,19
Answer:
6n - 5
Step-by-step explanation:
We find the jump between every 2 terms :
7 - 1 = 6
13 - 7 = 6
19 - 13 = 6
Now we know this will be the co-efficient of n and the 0th term will be added to the term :
1 - 6 = -5
So our final answer will be 6n + (- 5 ) = 6n - 5
Hope this helped and have a good day
=. Given function f(x)=x² − 3x+2, find f(x+h)-f(x) over
h
and simplify could someone please help on this ? Thanks !
What is the classification for this polynomial?.
-3m²n²
you factor the problem,
your answer:
-1x3xmxmxnxn
