The range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
Now, According to the question:
Let us consider the polynomial function as f(x) . Hence we need to find
[tex]T_5(x)[/tex] he formula for the Taylor series is:
[tex]T_n(x) =[/tex] Σ[tex]\left \{ {{n} \atop {j=0}} \right.}[/tex] [tex]\frac{f^(^f^)(a)}{f!}[/tex]
Suppose n =5, a=0 then
[tex]T_5 (x)= \frac{f(0)}{0!}(x -0)^0 + \frac{f'(0)}{1!}(x -0)^1+ \frac{f"(0)}{2!}(x -0)^2+...+ \frac{f^(^5^)(0)}{5!}(x -0)^5[/tex]
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
From the data:
f(x) = cos x => f(0) = cos(0) = 1
f'(x) = -sin x => f'(0) = -sin(0) = 0
f"(x) = -cos x => f"(0) = -cos(0) = -1
f"'(x) = sin x => f'"(0) = sin(0) = 0
f""(x) = cos x => f""(0) = cos0 = 1
f""'(x) = -sin x => f""'(0) = -sin(0) = 0
Substitute this data in the Taylor series:
[tex]T_5(x)=\frac{f(0)}{0!}+ \frac{f'(0)}{1!}x+\frac{f"(0)}{2!}x^{2} + \frac{f"'(0)}{3!}x^3+\frac{f""(0)}{4!}x^4+\frac{f^(^5^)(0)}{5!}x^5[/tex]
[tex]T_5(x) =\frac{1}{0!}+\frac{0}{1!}x+\frac{(-1)}{2!}x^{2} + \frac{0}{3!}x^3+\frac{1}{4!}x^4+\frac{(0)}{5!}x^5[/tex]
[tex]T_5(x) = 1 - \frac{1}{2!}x^{2} +\frac{1}{4!}x^4[/tex]
Now, the remainder of the Taylor series is Taylor series satisfies the following inequality.
[tex]|R_n(x)|\leq \frac{M}{(n +1)^1^!} (x-a)^n^+^1for|x+a|\leq d,here|f^(^n^+^1^)(x)|\leq M\\\\|x|\leq 1,a=0,n=5= > |f^(^6^)(x)|\leq 1[/tex]
Given that the approximation should be within 0.003712
Then,
[tex]\frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > \frac{1}{(6)}|x|^6\leq 0.003712\\ \\= > |x|^6\leq (0.003712)^6\\\\= > |x|^6\leq 0.022272\\\\|x|\leq (0.022272)^\frac{1}{6}\\ \\|x|\leq 0.5304[/tex]
Hence, the range of the values of x is
|x| [tex]\leq[/tex] 0.5304 [tex]\leq[/tex] 1
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The given question is incomplete , complete question is :
Find [tex]T_5(x)[/tex], the degree 5 Taylor polynomial of the function f(x) = cos(x) at
a = 0.
Find all values of x for which this approximation is within 0.003712 of the right answer. Assume for simplicity that we limit ourselves to |x| [tex]\leq[/tex] 1
____ 15. if gasoline costs $1.95 per gallon is its cost per liter? [1 quart = 0.946 liter]
If gasoline costs $1.95 per gallon $0.52 is its cost per liter?
One gallon of gasoline costs $1.95. To find the cost per liter, we need to convert gallons to liters. The conversion factor between gallons and liters is 1 gallon = 3.78541 liters.
So, to convert gallons to liters, we multiply the number of gallons by 3.78541.
In this case, the cost of one gallon of gasoline is $1.95. To find the cost per liter, we need to convert $1.95 from dollars per gallon to dollars per liter.
To do this, we divide $1.95 by the conversion factor between gallons and liters:
$1.95 / 3.78541
= $0.52/liter.
Therefore, the cost of one liter of gasoline is $0.52.
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What is simplest radical form in math?
The radical form of a number involves a square root. The number under the square root is a natural number or real number.
What is a radical?
The square root or nth root is represented by the symbol. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. An equation with radical expressions and variables as radicands is referred to as a radical equation.
The term "simplest radical form" refers to an algebraic expression's or number's most basic radical form. If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.
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Suppose you wanted to reach Alpha Centauri (4.4 ly from the Solar system) in 110 years. Pa How fast would you have to go in km/hr? Express your answer in kilometers per hour to two significant figures. v = 4.3x107 km/hr
the speed from kilometers per year to kilometers per hour 4.3x107 km/hr, the distance of 4.4 light years to kilometers.
1. First, convert the distance of 4.4 light years to kilometers.
1 light year = 9.46x1012 km
4.4 light years = 4.1x1013 km
2. Next, divide the distance by the time to calculate the speed:
Speed = Distance/Time
Speed = 4.1x1013 km/110 years
Speed = 3.7x1011 km/year
3. Finally, convert the speed from kilometers per year to kilometers per hour:
1 year = 8760 hours
Speed = 3.7x1011 km/8760 hours
Speed = 4.3x107 km/hr
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round answers to the nearest tenth
A. the value of x = 6.5( nearest tenth)
B. the value of x = 8.0 ( nearest tenth)
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Sin(tetha) = opp/hypotenuse
cos (tetha) = adj/hyp
tan (tetha) = opp/adj
in the first figure,
Tan22 = x/16
x =tan 22 × 16
x = 6.5(nearest tenth)
in the second figure,
sin42 =x/12
x = sin42× 12
x = 8.0 ( nearest tenth)
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which scale is based on tenths and hundredths of an inch?
The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes.
The formula for a decimal inch is 1 inch = 0.1 decimal inch. This means that every 0.1 decimal inch is equal to 1 inch. To calculate a decimal inch, simply divide the number of inches by 10. The decimal inch scale is based on tenths and hundredths of an inch. This scale is a common unit of measurement used for industrial, mechanical, and construction purposes. For example, if you have a measurement of 6 inches, the decimal inch measurement would be 0.6. You can also convert decimal inches to inches by multiplying the decimal number by 10. For example, if you have a measurement of 0.6 decimal inches, the inch measurement would be 6 inches.
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Find The Length S Of The Circular Arc. (Assume R = 6 And 0 = 126º.) S = O
The required length of the arc of the circle is approximately 13.08 cm.
What is arc?In mathematics, an arc is defined as a portion of the boundary of a circle or a curve. It can also be referred to as an open curve. The boundary of a circle is the perimeter or the distance around a circle, also known as the circumference.
According to question:The length of an arc of a circle is given by the formula:
L = θ * r / 180 * π
Where θ is the central angle in radians, r is the radius, and π is pi.
In your case, the radius of the circle is 6, and the central angle is 126°, so we need to first convert 126° to radians:
θ = 126° * π / 180 = 2.18 radians
Substituting the values in the formula, we get:
L = θ * r / 180 * π = 2.18 * 6 / 180 * π = 2.18 * 6 / π = 13.08 cm
So the length of the arc of the circle with radius 6 and central angle 126° is approximately 13.08 cm.
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Gabby uses a scissor to cut `\frac{5}{16}` inch off the top of a photo and `\frac{3}{8}` inch off the bottom. How much shorter is the total height of the photo now? Explain.
The length of the photo is shorter by 11/16 inches.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Top cutoff length = 5/16 inch
Bottom cutoff length = 3/8 inch
Now,
The length of the photo is shorter by:
= 5/16 + 3/8
= (5 + 6) / 16
= 11/16 inch
Thus,
The photo is shorter by 11/16 inches.
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When graphing "AND" inequalites, shading looks like____
When graphing "AND" inequalites, shading looks like Shading that always connects the 2 dots.
What is inequality?An algebraic statement that connects two values that are not equal is referred to as an inequality in mathematics. Inequality signals state that one of the two variables on either side of the inequality could be greater than, greater than or equal to, less than, or less than or equal to another value.
If a linear inequality has a sign that is either (less than) or, you will shade below the boundary line (less than or equal to). In a linear inequality, if the sign is > (greater than) or, you will shade above the boundary line (more than or equal to).
Follow these steps:
Rearrange the equation so "y" is on the left and everything else on the right.
Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
Shade above the line for a "greater than" (y> or y≥)
or below the line for a "less than" (y< or y≤).
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Write a compound inequality that represents the annual profits P ( in millions or dollars) from 2006 to 2013
Using inequality views, the compound inequality is given by:
50 ≤ P ≤ 90
An inequality is said to be compounded if it includes two terms, for example:a ≤ x ≤ b
Which has the following interpretation: x is more than a and x is less than b.From the graph, the minimum profit, in millions of dollars, was 50, in 2009.The maximum profit was 90, in 2012.From this, a compound inequality can be written, that the profit is more than 50 and less than 90, thus:50 ≤ P ≤ 90
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people attending a basketball game either supported the home team or visiting team. Of 2940 of the people attending supported the home team and 560 supported the visiting team, what percentage supported the home team?
The required 84% of the people attending the basketball game supported the home team.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
To find the percentage of people who supported the home team, we need to calculate the proportion of people supporting the home team and convert it to a percentage.
The total number of people attending the game is,
2940 + 560 = 3500.
The proportion of people supporting the home team is,
= 2940 / 3500
= 0.84.
To convert this proportion to a percentage, we multiply it by 100:
= 0.84 × 100 = 84%
Thus, 84% of the people attending the basketball game supported the home team.
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if an aircraft is certificated with 275 seats, but only 249 passengers are aboard for that flight segment, how many flight attendants are required? group of answer choices 6 4 7 5
5 flight attendants are required.
The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.
The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.
The number of flight attendants required can be determined by the following formula:
The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.
So, for an aircraft with 275 seats and 249 passengers:
(249 / 50) + 1
= 5 flight attendants are required.
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Miguel has 14 action videos and 21
adventure videos. Use a ratio to compare the number of action videos and the number of adventure videos.
The ratio of action videos to adventure videos is 14:21.
What is the ratio of action videos to adventure videos?This question uses the concept of ratios, which is a comparison of two or more values. Ratios are used to compare quantities in a variety of situations.
Count the number of action videos and the number of adventure videos. In this example, there are 14 action videos and 21 adventure videos.
Create a ratio by writing the number of action videos first, followed by a colon, followed by the number of adventure videos. In this example, the ratio is 14:21.
Simplify the ratio if needed. In this example, the ratio is already in its simplest form.
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What is the linear velocity in miles per hour of the tip of a lawnmower blade spinning at 3000 revolutions per minute in a lawnmower that cuts a path that is 24 inches wide?
Answer:v = ωr
v = speed in miles per hour (mph)
is the angle's speed in radians per hour.
r is the radius in miles.
(2400-rpm/60 minutes) =
(two radians per rev) Equals __ radians per hour
r=16 inches/2 = (8 inches)
(1/5280 miles/ft) (1/12 feet/in) = ______ miles
v = r = _ miles per hour
Step-by-step explanation:
v = ωr
v = speed in miles per hour (mph)
is the angle's speed in radians per hour.
r is the radius in miles.
(2400-rpm/60 minutes) =
(two radians per rev) Equals __ radians per hour
r=16 inches/2 = (8 inches)
(1/5280 miles/ft) (1/12 feet/in) = ______ miles
v = r = _ miles per hour
1. (D) Which of the following statements is true?
Explain your answer!
A.
B.
C.
13
19
13
19
13
19
2
2|22|3
Taking LCM and comparing the values we see that: 39/57 > 38/57. Hence, option C is the correct statement.
What is LCM?In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD).
When the fractions' denominators differ, LCM can also be used to add or subtract any 2 fractions. LCM is used to make the denominators common when doing any arithmetic operations using fractions, such as addition and subtraction.
The two values are:
13/ 19 and 2/3
Taking LCM we have:
13(3)/ 19(3) and 2(19) / 3(19)
39/ 57 and 38/57
Hence, comparing the values we see that:
39/57 > 38/57
Option C is the correct answer.
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a dog in an open field runs 12.0 m east and then 27.0 m in a direction 54.0 ∘ west of north. how far must the dog then run to end up 10.0 m south of her original starting point
A dog in an open field runs 12.0 m east and then 29.0 m in a direction 51.0 west of north, 69.50 south of east or 20.50 east of south must the dog then run to end up 10.0m south of her original starting point.
A dog in an open field runs 12.0 m east and then 27.0 m in a direction 54.0 degree west of north.
The dog's displacement vector is d(1) = [tex]12 \hat{i} + 29 [-sin51^{o} \hat{i} + cos51^{o} \hat{j}][/tex]
Thus, d(1) = [tex]12 \hat{i} + (-22.5 ) \hat{i} + (18.2) \hat{j}[/tex]
d(1) = [tex]-10.5 \hat{i} + 18.2 \hat{j}[/tex]
The dog's overall displacement is then
P = -10[tex]\hat{j}[/tex] - d(1)
P = [tex]-10 \hat{j} - [-10.5 \hat{i} + 18.2 \hat{j}][/tex]
P = [tex]10.5 \hat{i} - 28.2 \hat{j}[/tex]
The dog's direction is
θ = [tex]tan^{-1}[/tex][(28.2/10.5)]
θ = 69.50 south of east or 20.50 east of south
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List all values c guaranteed by the Mean Value Theorem forf(x)=x3+x2−4x+2on the interval[−1,3]
The Mean Value Theorem guarantees that the values of c for f(x)=x^3+x^2-4x+2 on the interval [1,3] are [7,9].
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.
Here,
f(c)=f'(b)-f'(a)/(b-a)
f(x)=x^3+x^2−4x+2
f'(x)=3x²+2x-4
x=-1, 3
f'(-1)=3-2-4
=-3
f'(3)=27+6-4
=29
f(c)=29+3/3+1
=32/4
f(c)=8
=[7,9]
The values of c guaranteed by the Mean Value Theorem for f(x)=x^3+x^2−4x+2 on the interval [−1,3] is [7,9].
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in a convex quadrilateral, the measure of the largest angle is twice the measure of the smallest angle, and the other two angles are both right angles. how many degrees are in the largest angle?
Answer: 90 degrees.
Step-by-step explanation:
Step 1: The smallest angle must be 90/2 = 45 degrees.
Step 2: The largest angle is twice the size of the smallest angle, so it is 90 degrees.
Jayden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
The number of cans are 9 and number of frozen food is 4.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Jayden bought cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium.
Let she bought x cans and y frozen food.
Therefore, establishing the equations,
x + y = 13
y = 13-x...(i)
200x + 650y = 4400...(ii)
Put eq(i) in eq(ii)
200x + 650(13-x) = 4400
200x + 8450 - 650x = 4400
450x = 4050
x = 9
Put x = 9 in eq(I)
y = 13-9
y = 4
Hence, the number of cans are 9 and number of frozen food is 4.
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now consider the situation when no two people get off at the same floor. before the elevator begins to travel, each of them pushes a button for his or her floor. in how many ways can the elevator buttons be lighted?
The number of ways the elevator buttons can be lighted is (m)(m-1)(m-2)...(m-n+1).
What is Permutations?
The mathematical notion of permutation describes the placement of things in a particular order. It is a method of determining how many unique configurations there are for a given set of objects.
If there are n persons in the elevator, and each one presses a button for a floor between 1 and m, what would happen? (inclusive). The number of permutations of m things taken n at a time, indicated as P, determines the number of ways the elevator buttons can be lit if no two individuals hit the same floor button and each person pushes a different floor button (m, n).
[tex]The formula for permutations is: P(m, n) = m! / (m - n)!.Therefore, the number of ways the elevator buttons can be lighted is:P(m, n) = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = m! / (m - n)! = (m)(m-1)(m-2)...(m-n+1).[/tex]
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The number of ways the elevator buttons can be lighted is [tex]m(m-1)(m-2)...(m-n+1)[/tex].
What are Permutations?
The placing of things in a specific order is described by the mathematical concept of permutation. It is a technique for figuring out how many different arrangements of a group of things there are.
It would be inclusive if there were n people in the elevator and each one pressed a button for a floor between 1 and m. If no two people press the same floor button and everyone presses a separate floor button, the number of P permutations of m items taken n at a time defines how many ways the elevator buttons can be lit (m, n).
The formula for permutations is:
[tex]P(m,n)=m(m-1)(m-2)...(m-n+1)[/tex]
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Erica is about to sign a lease for an apartment at a rate of $850 per month. She will need to pay the first month’s rent, the final month’s rent, and a $150 security fee. How much will her first payment be?
$1,000
$850
$1,850
$150
The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Rent = $850 per month
Security fee = $150
Then the amount of payment for the first month that Erica pays will be given as,
⇒ $850 + $150
⇒ $1,000
The amount of payment for the first month that Erica pays will be $1,000. Then the correct option is A.
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Angle b and angle c are complementary. If angle b is five times the size of angle c which equation can be used to find the measure of angle c?.
If angle b is five times the size of angle c, the equation can be used to find the measure of angle is 5x+x=90°.
because complementary angles complete each other to 90 degrees.
How to find equation aboveThese angles b and c add up to 90° because they are complementary.
Let's say angle C is named x.
angle b is five times the size of angle c, this can be written: 5x
Complementary angles add up 90°, so angle B add angle C equal 90°
the equation to find the measure of angle C is 5x+x = 90°.
Definition of AngleTypes of angles are one of the materials in mathematics that you always encounter at every level of education. Learning about angles is very important, because angles are always present in everyday life and need to be identified.
An angle is a shape formed by two rays having an endpoint at one point. In angles, terms such as the leg of the angle, vertex, and area of the angle are also found.
The legs of the angle are the lines forming the angle. The vertex is the point where the two legs of the angle intersect, and the area of the angle is the area bounded by the two legs of the angle.
Your question is incomplete but most probably your full question was:
Only Interaction Angle B and angle C are complementary: If angle B is five times the size of angle C which equation can be used to find the measure of angle C?
5x+x=180
5x = 180
5x+x=9
5x = 90
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Help Please!! thanksssss
The volume of the given object would be the addition of the volume of the cone and the volume of the rectangular prism = 3,648 in³.
How to calculate the volume of the object?The volume of cone = v = πr²h/3
where π = 3
r = 8/2 = 4ft
h = 12ft
Volume = 3× 4² × 12/3
= 576/3 = 192ft³
The volume of the rectangular prism = l×w×h
where;
l = 7ft
w = 2ft
h = 8ft
volume = 7×2×8 = 112ft³
Therefore the volume of the object = 192+112 = 304ft³
To convert to inches the following is carried out;
1 ft = 12 inches
304 ft = 304× 12 = 3,648 in³
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Figure ABCD has vertices A(1, 1), B(1, 4), C(4, 4), and D(4, 1). What are the coordinates of the vertices of Figure
A’B’C’D’ after a reflection across the line x = –2 and a translation 3 units up? Drag numbers to complete the coordinates.
Numbers may be used once, more than once, or not at all.
Answer:A(-5,4),B(-5,6),C(-7,6),D(-7,4)
Step-by-step explanation:If you draw a big enough graph it is easy to do.
Jimmy begins at the house. He walks to the horse barn. Then he walks 3 units up and 4 units right before returning back to the house. List the ordered pairs of the places jimmy visits in he order he visits them
There are 3 ordered pairs of the places jimmy visits in the order he visits them.
An ordered pair is a pair that is formed by two elements and are separated by a comma and written inside the parenthesis.
An example of ordered pair is (x,y).
where x is called the first element and y is called the second element of the ordered pair.
If we consider 2 order pairs the first-order pair is not equal to the second-order pair.
Example: (x,y) [tex]\neq[/tex] (y,x)
Now as per the diagram, jimmy has started at home next he walks to the horse which is the intersection of (1,1) points.
After then he walks 3 units up which is (1,3) which reaches the horse barn from that point he is supposed to move 4 units right and reached (5,6) At the Storage barn.
so the order pairs are:
(1,1) - At the house
(1,3) - At the horse barn
(5,6) - At the Storage barn
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ANSWERING ANY QUESTIONS FOR BRAINLIEST ANY QUESTION U MIGHT BE STUCK ON !!!
Step-by-step explanation:
Is power of mind is truee
The concept of the power of the mind is a widely debated topic, with varying opinions and perspectives. Some people believe in the power of positive thinking and visualization to achieve goals and create positive changes in one's life. Others may be more skeptical and question the scientific evidence supporting these ideas. Ultimately, whether or not the power of the mind is "true" is subjective and depends on one's personal beliefs and experiences.
Describe all solutions of Ax = 0 in parametric vector form, where A is row equivalent to the given matrix. [2 -1 -4 2 6 -3] x = x_2 + X_3 (Type an integer or fraction for each matrix element.)
A general solution to the system Ax = 0 in parametric vector form is given by:
X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]
How to find all solutions of Ax = 0 in parametric vector form?The matrix [2 -1 -4 2 6 -3] can be row-reduced to the row-echelon form [2 -1 -4 0 6 -9], which has a pivot in the first, second and fourth columns. This implies that the columns with zero entries in the row-echelon form correspond to free variables in the solution.
Since there are two free variables in the row-echelon form, the solution to the homogeneous linear system Ax = 0 will be in the form of a parametric vector, where X_2 and X_3 are the free variables and X_1, X_4, and X_5 are expressed in terms of X_2 and X_3.
A general solution to the system Ax = 0 in parametric vector form is given by:
X = X_2 * [1 0 1 0 0] + X_3 * [0 1 0 1 0]
where X_2 and X_3 are arbitrary constants. This represents a two-dimensional subspace in R^5, which consists of all linear combinations of the two linearly independent vectors [1 0 1 0 0] and [0 1 0 1 0].
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what is the answer for this maths watch question?
Answer: 7
Step-by-step explanation:
Combine like terms
7^15/7/^14 = 7
(1 point) solve the division problem ⎡⎣⎢4−4−40−1−100−1⎤⎦⎥⎡⎣⎢xyz⎤⎦⎥=⎡⎣⎢−434⎤⎦⎥
The solution to the division problem is xyz = −434 with a remainder of 0.
The given equation is [tex]$\frac{4-4-40-1-100-1}{xyz} = -434$[/tex]. To solve this equation, we need to find the value of [tex]$xyz$[/tex]. We can use the distributive property to break up the numerator, yielding [tex]$\frac{(-1)(-100)(-1)}{xyz} = -434$[/tex]. Then, we can multiply both sides by [tex]$xyz$[/tex] to get [tex]$(-1)(-100)(-1)xyz = -434xyz$[/tex] . Since the terms on both sides of the equation are equal, we can simplify to [tex]$(-1)(-1)(-100)xyz = -434xyz$[/tex] . Now, we can factor out the xyz, which yields [tex]$xyz(-1)(-1)(-100) = -434xyz$[/tex]. Since we want to find the value of xyz, we can divide both sides by the common factor of xyz, yielding [tex]$(-1)(-1)(-100) = -434$[/tex] . Finally, we can solve for xyz by multiplying both sides by the common factor of (-1)(-1)(-100), yielding xyz = -434. Therefore, the value of xyz in the given equation is -434.
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Maria had $160. She spent 3/8 of her money at the supermarket and 1/4 of it at the hair salon. How much did Maria spend?
Maria spent $100 in total. She spent $60 at the supermarket and $40 at the hair salon.
Explanation:This problem involves calculations with fractions. Maria had $160. She spent 3/8 of it at the supermarket and 1/4 of it at the hair salon. To find out much money she spent, add the fractions and then multiply the result by the total amount of money she had.
To find how much Maria spent at the supermarket, multiply $160 by 3/8: 160 * 3/8 = $60.
To find how much Maria spent at the hair salon, multiply $160 by 1/4: 160 * 1/4 = $40.
Now, add the amounts spent at the supermarket and the hair salon: $60 + $40 = $100. So Maria spent $100 in total.
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Question 3 of 10
Find the solution(s) to x2 - 12x + 36 = 0.
A. x = 6 and x = -6
B. x = 6 only
C. x = 4 and x = 9
OD. x = -2 and x = 18
SUBMI
Answer: B. x=6 only
Explanation: A fast way to check these kind of multiple choice questions is to just plug in one of the values into the equation and see if it works. For example you can put (6^2)-(12×6)+36 and it would equal 0 making the equation true. All other options wouldn't have equaled 0 so it would make x=6 the only right option.