The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option c)
Suppose we are given a quadratic function f(x) = ax² + bx + c, then x = q is a root if f(q) = 0.
Let's check for the given functions:
a. x² - 4x + 5 = 0
f(2) = 2² - 4(2) + 5
f(2) = 4 - 8 + 5 = 1
Since f(2) ≠ 0, hence 2 is not its root.
b. x² + 3x - 12 = 0
f(2) = 2² + 3(2) - 12
f(2) = 4 + 6 - 12 = -2
Since f(2) ≠ 0, hence 2 is not its root.
c. 2x² - 7x + 6 = 0
f(2) = 2(2)² - 7(2)+ 6
f(2) = 2(4) - 14 + 6 = 0
Hence, x = 2 is its root.
d. 3x² - 6x - 2 = 0
f(2) = 3(2)² - 6(2) - 2
f(2) = 12 - 12 - 2 = -2
Since f(2) ≠ 0, hence 2 is not its root.
Hence, the correct option is 2x² - 7x + 6 = 0 (option c)
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Points A, B, C, D, E, F and G are on a number line such that B, C, D, E and F divide segment AG into 6 equal pieces. If A is at 13 and G is at 59, what is the sum of the numbers at B, C, D, E and F
The sum of numbers at B, C, D, E and F is 110.5
Since B, C, D, E, and F divide the segment AG into 6 equal pieces, each piece has a length of (59-13)/6 = 6.5.
Therefore, the numbers at B, C, D, E, and F are located at 13 + 6.5, 13 + 6.52, 13 + 6.53, 13 + 6.54, and 13 + 6.55 respectively.
The sum of the numbers at B, C, D, E and F is (13 + 6.5) + (13 + 6.52) + (13 + 6.53) + (13 + 6.54) + (13 + 6.55)
= 13 + 6.5*(1+2+3+4+5) = 13 + 6.5*15 = 13 + 97.5
= 110.5
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals. All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.
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Select all the inequalities that have symbols that will be reversed when the variable is isolated.
–10. 5 < 3a
b6 ≤ 7
–4. 5c > 9
–215 ≤ –52d
e – 13 ≥ 11
Option - C and D : -4.5c > 9 and -215 ≤ -52d will have its inequalities that have symbols that will be reversed when the variable is isolated .
Anytime you are multiplying or dividing an inequality by a negative you must reverse the inequality symbol .
Inequalities in mathematics specify the connection between two non-equal quantities. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.
The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples. "A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">,",“<”, “≥”, “≤”, An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions.
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A photographer prints an 8x10 team photo. The team would like to get it blown up by 200% in order to display it in the trophy case. What will be the new dimensions of the photo?
Answer:
16x20
Step-by-step explanation:
I think, 200% likely means x2. Just an idea, try it if you'd like!
Cuál es la raíz cuadrada de 169
El número natural 169 tiene como raíz cuadrada igual a 13.
¿Cómo encontrar la raíz cuadrada de un número entero?Los números naturales comprenden a un conjunto discreto conformado por los números {1, 2, 3, 4, 5, ..., n, ...}, n ∈ N, donde N es el conjunto de los números naturales.
Los números naturales pueden ser números primos o números compuestos, los números compuestos pueden ser definidos como un producto de números primos. El número natural 169 es equivalente al siguiente producto de números primos:
169 = 13 × 13 = 13²
En consecuecia, la raíz cuadrada del número natural 169 es la siguiente: (nótese que la potencia al cuadrado es el opuesto a la raíz cuadrada)
x = √169
x = √(13²)
x = (13²)^(1 / 2)
x = 13
La raíz cuadrada del número natural 169 es igual a 13.
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Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded.
Therefore ,option C is correct since the percentage sample would need to be higher than 100 to produce a significant result.
What is a percentage?A percentage is a subdivision by 100, also referred to as percent. A percentage, which is defined as "per 100," denotes a component of an overall amount. For instance, 45% represents the number 45 out of 100. Calculating a percentage is the process of finding the proportion of a whole given terms of 100. There are choices for fraction computation and using online calculators.
Given:
A random selection of 75 drug users of drug X and just a random selection of 150 drug users of drug Y are chosen,
Most statisticians agree that you need a 100 sample size to get any kind of statistically meaningful findings. You should absolutely poll each and every person in a population of less than 100.
The representative sample for medication X is therefore insufficient.
Therefore ,option C is correct since the sample would need to be higher than 100 to produce a significant result.
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Determine the value of x using a trigonometric ratio. Question 9 options: A) 4.98 B) 4.18 C) 10.11 D) 8.49
Using the trigonometric ratios the correct option is option a) 4.98.
We have a known hypotenuse, but an unknown opposite side. Use the sine ratio to tie the two together to be able to solve for x.
Trigonometric ratios are a set of ratios that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
These ratios can be used to find missing side lengths or angle measures in a right triangle, and they have many applications in mathematics, physics, engineering, and other fields.
sin(angle) = opposite/hypotenuse
sin(50) = x/6.5
6.5*sin(50) = x
x = 6.5*sin(50)
x = 4.97928888027336, make sure your calculator is in degree mode
x = 4.98
Therefore, Using the trigonometric ratios the correct option is option a) 4.98.
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03.06 LC)
Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 7 and b = 10?
The standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
What is Hyperbola ?
a plane curve generated by a factor so moving that the difference of the distances from two constant points is a consistent : a curve formed by way of the intersection of a double right circular cone with a plane that cuts each halves of the cone.
Given,
The standard equation of the hyperbola centered at the origin with given values a=7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
vertical axis with values a = 7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
(x^2 / 7*7) - ( y^2/ 10*10) = 1
x^2 / 49 - y^2 / 100 = 1
Hence , the standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
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The surface area of this cone is 5,633.16 square millimeters. What is the slant height of this
cone?
Use ≈ 3.14 and round your answer to the nearest hundredth,
Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm.
Definition of surface areaHow much surface area it occupies is a decent indication of its total size. The surroundings is taken into account while calculating the squared of a right triangle. Anything's overall size is determined by its surface area. The volume of water inside a cuboid is the total of the volumes on each of the six horizontal sides. To determine the box's dimensions, use the formula below: The region is the same in 2lh, 2lw, and 2hw (SA). The overall area of the adaptable shape serves as a representation of the region.
Here,
Given :
Surface area = 5633.16 square millimeters
and
slant height = x
radius = 26 mm
So,
=> SA = πr² + πrl = 5633.16
=>SA = π(r² + rl) = 5633.16
=> SA = 3.14 ( 26² + 26* l) = 5633.16
=> SA = 2122.64 + 81.64l = 5633.16
=> SA = 81.64* l = 5633.16 - 2122.64
=> 81.64*l = 3510.52
=> l = 3510.52/81.64
=> l = 43 mm
Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm .
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ft.
2. A slow-moving bug is climbing a 15 ft. pole to reach a critical food source. It manages to climb 3
each day, but at night it slides back down 1 ft. How many days will it take the bug to reach the top and
get the food?
Step-by-step explanation:
a0 = 0 ft (starting on the ground)
a1 = a0 + 3 - 1 = a0 + 2
an = an-1 + 3 - 1 if an-1 +3 < 15
an = an-1 + 3 if an-1 + 3 >= 15
so, we need to find the n, so that
an = an-1 + 2 >= 12
but by looking at the structure, we see that every step just adds 2 ft to the total height.
an = a0 + 2n = 0 + 2n = 2n
2n >= 12
n >= 6
so, with day 6 the bug reaches 12 ft height. in day 7 it gets up to 15 ft and reached its goal.
it will take 7 days for the bug to reach the top and get the food.
A cell phone plan cost $27.70 per month for 500 minutes of talk time. It cost an additional $0.08 per minute for each minute over 500 minutes. To get email access, it cost 30% of the price for 500 minutes of talk time. Your bill, which includes email, is the same each month for 9 months. The total cost for all 9 months is $367.29. Write and solve an equation to find the number of minutes of talk time you use each month.
Answer:
567 minutes each month.
Step-by-step explanation:
Let x be the number of minutes of talk time used each month.
The cost for talk time beyond 500 minutes is $0.08 * (x - 500)
The cost for email is $27.70 * 0.3 = $8.31
The total monthly cost is $27.70 + $0.08 * (x - 500) + $8.31 = $35.99
The total cost for 9 months is $35.99 * 9 = $323.91
So we can set up the equation:
$27.70 + $0.08 * (x - 500) + $8.31 * 9 = $367.29
Solving for x, we get:
x = 567
So the number of minutes of talk time used each month is 567 minutes.
A cloud is drifting across the sky at 552metersperminute. it is at an altitude of 9,200 meters. if its speed remains steady, how far will the cloud move in 17.5minutes?
The cloud can ascend 9,616 metres in 17.5 minutes, based on the statement made.
How is altitude measured and what does it mean?Utilizing the measurement of air pressure, altitude may be calculated. The pressure decreases with increasing altitude. An instrument is referred to as a pressure analyzer or pneumatic altimeter when a barometer is given a nonlinear calibration to display altitude.
This may be calculated by dividing the cloud's speed (552 metres per minutes) by the distance it must travel (17.5 minutes). We now know the distance to be 9,616 meters.
The speed of said cloud and the length of time it is going are four pieces of information that must be known in order to determine the minimum distance the cloud might cover in 17.5 minutes. We must increase the cloud's stated speed of 552 meters a minute by the distance it is going across, which in itself is 17.5 minutes. As a result, we now have 9,616 meters overall.
Another way to see this is to picture the cloud beginning at place A (9,200 meters) or terminating at point B. (9,616 meters). The distance between points A and B will be covered in 17.5 minutes if the cloud is moving at a pace of 552 meters per minute.
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3x − (2x² +1 − 8x) − (3x − 2x² + 7)
Answer: The answer is 5x
Answer: x=1
Step-by-step explanation:
=3x-[tex]2x^{2}[/tex]-1+8x-3x+[tex]2x^{2}[/tex]-7
= -1+8x-7
= -8=-8x
X=1
How do I solve this?
The evaluation of the piecewise function gives:
when x = -3, f(x) = -4; when x = 2, f(x) = 0; and when x = 4, f(x) = 2.
when x = -3, w(x) = 2; when x = 2, f(x) = 5; and when x = 4, f(x) = 5
How to evaluate a piecewise function?A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.
We want to evaluate the piecewise function when x = -3, x =2 and x = 4:
{ -4, x < 2
f(x) = { x-2, -2 ≤ x≤ 4
{0 x > 4
when x = -3:
f(x) = -4 because x < 2 (i.e. -3 < 2)
when x = 2:
f(x) = x-2
f(2) = 2-2 = 0
when x = 4:
f(x) = x-2
f(2) = 4-2 = 2
{ -x - 1, x ≤ -3
w(x) = { 2x + 2, -3 < x < 2
{5, x ≥ 2
when x = -3:
w(x) = -x - 1
w(-3) = -(-3) - 1 = 2
when x = 2:
f(x) = 5
when x = 4:
f(x) = 5
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For each sequence find the first 4 terms and the 10th term.
A)n^2+6
B)3n^2
The first 4 terms and the 10th term of the sequences are listed below
How to determine the terms of the sequenceFrom the question, we have the following parameters that can be used in our computation:
Calculate the first 4 terms and the 10th term.
A)n^2+6
Here, we have
First = 1^2 + 6 = 7
Second = 2^2 + 6 = 10
Third = 3^2 + 6 = 15
Fourth = 4^2 + 6 = 24
Tenth = 10^2 + 6 = 106
B)3n^2
Here, we have
First = 3 * 1^2 = 3
Second = 3 * 2^2 = 12
Third = 3 * 3^2 = 27
Fourth = 3 * 4^2 = 48
Tenth = 3 * 10^2 = 300
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suppose that you draw a card from a standard deck of cards. what is the probability that the card is a face card (i.e., a jack, queen, or king) or a heart?
The probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13
In the given question, suppose that you draw a card from a standard deck of cards.
We have to find the probability that the card is a face card (i.e., a jack, queen, or king) or a heart.
As we know that in a deck of cards have total 52 cards.
In which 26 cards are in heart shape.
Every different type of card have 3 face cards and have total four different type of cards. That means there are total 12 face cards.
In 26 cards of heart have total 6 face cards.
So, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart
P = (Total face cards + total heart shape card - 6 face cards)/Total cards in a deck
P = (12 + 26 - 6)/52
P = (38 - 6)/52
P = 32/52
P = 8/13
Hence, the probability that the card is a face card (i.e., a jack, queen, or king) or a heart is 8/13.
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bags of clementines have 12 each. for a party, sal, trisha, and joe each brought bags of clementines. altogether, there were 180 clementines. sal brought 4 bags and joe brought 6. write the equation to determine how many bags trisha brought, t.(2 points)
The equation to determine how many bags Trisha brought is: T = 180 - (4 + 6)
We know that the total number of clementines is 180, Sal brought 4 bags and Joe brought 6. To determine how many bags Trisha brought, we need to determine the total number of bags that Sal and Joe brought together. We can do this by combining the two numbers together (4 + 6). This will give us a total of 10 bags. To determine how many bags Trisha brought, we need to subtract the total number of bags that Sal and Joe brought (10) from the total number of clementines (180). This gives us an answer of 170. This means that Trisha brought 170 clementines, or 7 bags. Therefore, the equation to determine how many bags Trisha brought is: T = 180 - (4 + 6).
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22/3 times x = 1.6 divided by 6/11
PLS HELP
[tex]\cfrac{22}{3}x=\cfrac{1.6}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{\frac{16}{10}}{~~ \frac{6 }{11 } ~~}\implies \cfrac{22x}{3}=\cfrac{16}{10}\cdot \cfrac{11}{6}\implies \cfrac{22x}{3}=\cfrac{8}{5}\cdot \cfrac{11}{6}[/tex]
[tex]\cfrac{22x}{3}=\cfrac{8}{6}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{4}{3}\cdot \cfrac{11}{5}\implies \cfrac{22x}{3}=\cfrac{44}{15} \\\\\\ \stackrel{\textit{multiplying boths sides by }\stackrel{LCD}{15}}{15\left( \cfrac{22x}{3} \right)=15\left( \cfrac{44}{15} \right)}\implies 110x=44\implies x=\cfrac{44}{110}\implies \boxed{x=\cfrac{2}{5}}[/tex]
√2x+5=5 then the value of x
Answer:
x = 0Step-by-step explanation:
√2x + 5 = 5
-5 - 5
√2x = 0
√2x^2=0^2
2x=0
2x/2 = 0/2
x = 0[tex]\huge\red{ANSWER}[/tex]
[tex]\sf \sqrt{2} x+5=5[/tex]
[tex]\sf \sqrt{2} x=5-5[/tex]
[tex]\sf \sqrt{2} x = 0[/tex]
[tex]\sf \frac{\sqrt{2} x }{2}=0[/tex]
[tex]\sf x=0[/tex]
________......
[tex]\pmb{ \orange{LearningLifeII}}[/tex]
Which of the following tables represents a multiplicative relationship?
Answer:
B is the answer
Step-by-step explanation:
A multiplicative relationship means that 2 quantities can be expressed as multiples of each other
The owner of a pet food store wants to mix birdseed that cost $1.25 per pound with sunflower seeds that cost $0.75 per pound to make 50 pounds of a mixture that cost one dollar per pound how many pounds of each type of sea should he use
If the owner of a pet food store wants to mix birdseed that cost $1.25 per pound with sunflower seeds that cost $0.75 . The number of pounds of each type of sea he should use is: 25 pounds of $1.25 birdseed and 25 pounds of $.75 sunflower seed.
How to find the number of pounds?Let x represent the number of pounds of $1.25 birdseed that is is used
1.25x+.75(50-x)=50×1
1.25x+37.5-.75x=50
Combine like terms
.50x=50-37.5
.50x=12.5
Divide both side by .50x
x=12.5/.5
x=25 pounds of $1.25 birdseed
So,
50-25=25 pounds of $.75 sunflower seed
Therefore the number of pounds is $1.25 birdseed and $.75 sunflower.
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Evaluate
2a + 16
3b
when a = 3 and b = -2
Answer:
2a + 16
2(3) + 16
6 + 16 = 22
3b
3(-2) = -6
Step-by-step explanation:
Substitue the appropriate values into the expressions.
An equilateral triangle and an isosceles triangle share a common side. What is the measure of ∠ ABC?
The measure of ∠ ABC is 112°
How determine the measure of ∠ ABC?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a shape with its angles.
Triangle BCD is an equilateral triangle. So all the angles are equal, that is 60° each.
∠ ADB = 64° (base angle of an isosceles triangle are equal)
∠ ABD = 180° - 64° - 64° (sum of angles in a triangle is 180°)
∠ ABD = 52°
∠ ABC = ∠ ABD + ∠ CBD
∠ ABC = 52° + 60°
∠ ABC = 112°
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Helllllp please thank you
Step-by-step explanation:
A no
n + 7 = 16
n + 7 - 7 = 16 - 7
n = 9
that is not n = 15
B yes
(2/3)v = 8
3×(2/3)v = 3×8
2v = 24
2v/2 = 24/2
v = 12
C no
6z = 84
6z/6 = 84/6
z = 14
that is not z = 8
5x+6=7x-6
Please help
Answer:
x = 6
Step-by-step explanation:
5x+6=7x-6
-6 -6
--------------------
5x = 7x - 12
-7x -7x
--------------------
-2x = -12
------------
-2 -2
--------------------
x = 6
Answer:
6
Step-by-step explanation:
first we combine like terms
6+6=7x-5x
then we simplify
12=2x
lastly we divide both sides by 2
2x ÷2=12÷2
an we simplify again
x=6
then the value of x is 6
check
5(6)+6=7(6)-6
30+6=42-6
36=36
a rectangle has its base on the x acis and its upper two vetivies on th eporabloa 16-x^2what is the maximum area the rectangle can have
The maximum area the rectangle can have, is 2.31 square unit.
In the given question, a rectangle has its base on the x axis and its upper two vertices on the parabola 16 - [tex]x^2[/tex].
We have to find the maximum area the rectangle can have.
Let Length is x and width is y.
So, Area of Rectangle = length × breadth
Area of Rectangle = xy
Since, base is on the x - axis, therefore, length will be 2x.
Now, Area of Rectangle = 2xy
The given parabola y = 16 - [tex]x^2[/tex]
Area of Rectangle = 2x(16 - [tex]x^2[/tex])
Area of Rectangle = 32x - 2[tex]x^3[/tex]
For Largest Area find derivative of Area and set equal to zero.
A'(x) = 32 - 6[tex]x^2[/tex]
Now equating equal to zero
32 - 6[tex]x^2[/tex] = 0
Subtract 32 on both side, we get
- 6[tex]x^2[/tex] = - 32
Divide by -6 on both side, we get
[tex]x^2[/tex] = 5.33
Taking square root on both side, we get
x = 2.31
Hence, the maximum area the rectangle can have, is 2.31 square unit.
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a gym class has $12$ students, $6$ girls and $6$ boys. the teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. if the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys? (jerseys of the same color are indistinguishable.)
So, the teacher can give out the jerseys in 840 ways.
The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.
One possible way to count the number of ways to divide the students is to use the stars and bars method.
For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:
(5+2)!/(5!2!) = 7
For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:
(4+1)!/(4!1!) = 5
For the third team, we have 3 stars, so the number of ways to pick 6 students is:
(3+0)!/(3!0!) = 4
Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:
7 * 5 * 4 = 140
Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:
140 * 3! = 840
Therefore, the teacher can give out the jerseys in 840 ways.
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if justin randomly chooses his ride in the morning and in the evening, what is the probability that he'll use both the bus and the train?
The probability that he'll use both the bus and the train is 0.2222
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .
There are just two ways in which Justin use both the bus and the train on the same day:
1. He used bus in the morning and train in the evening
2. He used train in the morning and bus in the evening
Additionally, every day he has 9 possible ways to used the transportation, 3 in the morning multiply by 3 in the evening. This is:
3 * 3 = 9
p= 0.222
So, the probability is calculate as a division between the possible ways in which he use both transportations and the total possible ways. This is:
p=0.222
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A 2-pound bag of carrots costs $6.40. What is the price per ounce?
Belinda is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years:
Answer:
A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Part A :
If a function is linear, then the function values have equal differences.
If a function is exponential, the function values have equal ratios.
For car 1 :
36450 / 40,500 = 9/10
32805 / 36450 = 9/10
Values of car have equal ratios.
This is exponential function.
For car 2 :
39000 - 42000 = -3000
36000 - 39000 = -3000
Values of car have equal differences
This is linear function.
Part B :
The initial value of car is 45,000.
For car 1 :
f(1) = 40,500, f(2) = 36,450, ............
For car 2 :
f(1) = 42,000, f(2) = 39,000, ..........
Part C :
For car 1 :
f(13) = = 11438.396
For car 2 :
f(13) = = 6000
There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.
Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.
Step-by-step explanation:
List five vectors in Span {v1,v2}. Do not make a sketch.v1=6 4 −8v2=−6 2 0
The five vectors in span {v1,v2} are we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together.
1. v3 = (3v1 + 2v2) = (18 8 −16)
2. v4 = (2v1 + 3v2) = (−12 6 0)
3. v5 = (4v1 + v2) = (0 6 −32)
4. v6 = (−2v1 + 5v2) = (36 10 0)
5. v7 = (−v1 + 4v2) = (−36 8 0)
To calculate the vectors, we first multiply each vector component (x, y, and z) of v1 and v2 by a constant and then add them together. For example, for v3 we multiplied v1 by 3 and v2 by 2 and then added the components together to get the vector (18 8 −16). We performed similar calculations for the other vectors.
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