Answer:
Not a triangle.
Criteria for it to be a triangle:
3 = A
6 = B
2 = C
A + B > C
B + C > A
A + C > B
What this says, is that if you add any two sides of the triangle, it needs to be bigger than the one you left out.
3 + 6 > 2 This one works
6 + 2 > 3 This one works
3 + 2 > 6 This one doesn't work because 5 is less than 6
Since the last one didn't work, it's not a triangle.
can someone help me with this thank you
Step-by-step explanation:
we know that the two angles with x are equal since they are made with the same lines
so
8x+36=5x+51
solve for x
a. subtract 36 from both sides
8x=5x+15
b. subtract 5x on both sides
3x=15
c. divide by 3
x=3
now to find z
we know a line equals 180
so
(8x+36)+z=180
plug in 3
8(3)+36+z=180
24+36+z=180
60+z=180
z=120
Phoebe had $14.27. Then she earned $8.75 for raking her neighbor's leaves.
How much money does she have now?
Answer:
$23.02
Step-by-step explanation:
You add what she earned to what she had before
$14.27 + $8.75 = $23.02
A circle with center C has equation x²+y²- 2x + 10y-19 = 0
It can be shown that center C is (1,-5) and that the radius is √45.
Find the equation of the tangent to the circle at the point (7,-2), giving your answer in the form ax + by + c=0, where a, b and c are integers.
Answer:
2x + y - 12 = 0
Step-by-step explanation:
The Tangent line will Always be perpendicular to the radius of a circle.
1. Find the slope of the radius that goes from the Center to the given point:
[tex]m=\frac{-2--5}{7-1}=\frac{3}{6}=\frac{1}{2}[/tex]
2. The slope of the Tangent at (7,-2) is the Negative (opposite) Reciprocal of the slope of the radius: [tex]\frac{1}{2}= > -2[/tex]
3. Write the equation of the Tangent in Point Slope Form:
[tex]y+2=-2(x-7)[/tex]
4. Distribute and rewrite in the form ax + by + c = 0
[tex]y+2=-2(x-7)\\y+2=-2x+14\\2x+y-12=0[/tex]
Given: C is the midpoint of DA and FE bisects LAED. List three congruence statements and reasons based on
the given information.
Triangles ΔAEC, ΔECD are congruent.
What are conditions of Congruency?Three angles and three sides, or the six measuring components, specify the requirements for the congruence of triangles. But if three of these are correctly satisfied, the other three are also satisfied automatically. Axioms for congruency are four such instances.
Triangles are said to be congruent if:
Congruent triangles under the SSS (Side Side Side postulate) condition.
Congruent triangles criterion according to the SAS (Side Angle Side postulate).
Congruent triangles are a requirement of the ASA (Angle Side Angle postulate).
The congruent triangles criterion of the AAS (Angle Angle Side postulate).
Given C is mid point of AD.
and, FE bisects the angle ∠AED.
By SAS Postulate we can say ΔAEC, ΔECD are congruent.
In triangles ΔAEC, ΔECD;
AC=CD (C is mid point)(S);
∠CEA=∠CED (Bisector)(A)
CE=CE (Common side)(S);
So by SAS theorem both are Congruent.
Triangles ΔAEC, ΔECD are congruent.
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you have a bag of ping pong balls. you arrange all but 2 of the balls in an equilateral triangle. then you put all the balls back into the bag and create a new equilateral triangle where each side has one more ball than the first arrangement but this time you are 11 balls short. how many balls were in the first arrangement?
Answer:
The “edge” effect of a tetrahedral container with edge length of 1,000 mm would be 2*r*√3 (r = radius of ball, see diagram below). For a ping pong ball with a diameter of 40 mm, the edge effect would be 2*20*√3 = 69.28 mm. Subtract that from 1,000 mm and you get 930.72 mm of “available space” along the bottom row. Divide 930.72 mm by 40 mm per ball and you get 23.27. So you wouldn’t be able to fit 24 balls along the base, you’d only be able to fit 23 balls. With 23 balls, the total number that a tetrahedron could contain (T) would be T = n(n+1)(n+2)/6 = 2,300 balls, not 2,600.
An architect built a scale modelof a sports stadium using a scale in which 2 inches represents 30 feet.The height of the sport stadium is 180 feet.What is the height of the scale model in inches?
The scale model of the sports arena has a height of 12 inches.
What does unit rate mean?Unit rate is the amount of something at a rate of one amount to another amount.
If 2 inches = 30 feet, then a sports stadium's height is 180 feet.
A man can walk 6 kilometers in 2 hours.
A man can cover 3 miles by walking in an hour.
A machine can cut 10 potatoes in five minutes.
A machine can cut two potatoes in a minute.
30 feet equals 2 inches.
Add 30 to both sides.
1 foot equals 2/30 inches.
1 foot equals 2/30 inches today.
Add 180 to both sides.
180 feet equals 180 x 2/30 inches.
6 × 2 inches times 180 feet.
12 inches equal 180 feet
Since the height of the sports stadium is 180 feet, 2 inches would equal 30 feet.
The scale model of the sports arena has a height of 12 inches.
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After a snowball fight, Nathan wanted to warm up with a cup of hot chocolate. He decided to make enough to share with his friends. First, he heated 6 cups of milk and 1 pint of cream in a large pot. Then, he stirred in 4 cups of melted chocolate. How many cups of hot chocolate did Nathan make?
The number of cups of hot chocolate drink Nathan made is 12 cups.
How many cups of hot chocolate did Nathan make?Number of cups of milk Nathan heated = 6 cupsNumber of cups of melted chocolate = 4 cupsNumber of cream = 1 pintConvert pint to cup:
1 pi-nt = 2 cups
Total cups of hot chocolate Nathan made = Number of cups of milk Nathan heated + Number of cups of melted chocolate + Number of cream
= 6 + 4 + 2
= 12 cups
Therefore, Nathan made 12 cups of hot chocolate drink.
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Which of the following inequalities matches the graph? (1 point) −6x + y < 3 6x + y < 3 6x − y < −3 The correct inequality is not listed
6x − y < −3 , inequality matches the graph.
Step 1:
Find the equation of the line
we have A(0,3) , B(1,9)
The formula to calculate the slope between two points is equal to
m = (y₂-y₁) / (x₂-x₁)
Substitute the values:
m = (9-3) / (1-0)
m = 6/1
m = 6
The equation of the line into slope intercept form is equal to
y = mx + c
where
m is the slope
b is the y-intercept
In this problem we have
m = 6
b = 3 ----> the y-intercept is the point B
Substitute the values:
y = 6x + 3
Step -2
Find the equation of the inequality
we know that:
The solution is the shaded area above the dashed line
so, the inequality is equal to
y > 6x + 3
rewrite
-6x + y > 3
6x - y < -3
Step 3
Using a graphing tool
The x-intercept is the point
The y-intercept is the point
The slope of the dashed line is positive, the graph in the attached figure.
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4 divide 5/6 as a mixed number ??
Answer: exact form is 24/5, decimal form is 4.8 and mixed number form is 4 4/5
Step-by-step explanation:
Answer:
4 4/5 (simplified)
Step-by-step explanation:
Using reciprocals:
4 divided by 5/6 = 4 x 6/5
= 24/5 = 4 4/5
To check: 4 4/5 x 5/6 = 4
You can use the same method for similar problems
A triangle has side lengths of 200 units and 300 units. Write a compound inequality for the range of the possible lengths for the third side,
Answer:
100<x<500
Step-by-step explanation:
We can create a system of inequalities by using the Triangle Inequality Theorem. This theorem states that the sum of two sides on a triangle is greater than the other sides.
1.) Figure out the first inequality. This would be 300+200>x, or x<500.
2.) Figure out the second inequality. This would be x + 200 > 300, or x>100.
3.) Figure out the third inequality. This would be x + 300 > 200, or x > -100.
4.) Combine these inequalities. By combining these inequalities, we would get 100<x<500.
mean of 8,7,11,15,3,4
Answer:
8
Step-by-step explanation:
The mean of numbers is the sum of the numbers divided by the number of numbers. By this definition, we first have to add up all of these numbers. If we do, we get 48. Now, we figure out the number of numbers, which is 6. Finally, we divide 48 by 6 to get 8.
The number line includes points A, B, C and D which statement is true.
Answer:
yes youre right it is point D
Step-by-step explanation:
9. Delia bought $45 dollars worth of clothes, but the total including sales tax came to $54. What is
the sales tax rate that Delia paid?
of the vehicles
Answer:
20%
Step-by-step explanation:
You want to know the tax rate if the added tax brings the cost of $45 purchase to a total of $54.
MultiplierThe multiplier applied to a purchase cost to add the tax is ...
(1 +r)
where r is the tax rate.
Here, that means ...
45(1 +r) = 54
1 +r = 54/45 = 1.20
r = 1.20 -1 = 0.20 = 20%
The tax rate Delia paid on the articles she bought was 20%.
Kim ran a 26-mile marathon.
She ran 1/7 of the marathon during
the first hour. How many miles did
Kim run during the first hour?
Answer:3.71 miles
Step-by-step explanation:
TEXT ANSWER
An airplane has stopped to refuel. Fuel is being added to the plane's gas tank at a constant
rate. After 13 minutes, there are 32,882 gallons of fuel in the plane; after 31 minutes, there
are 34,902.5 gallons in the plane. Write the y = mx + b equation that describes this
scenario.
W
You can refer to time 31:05 in the video above for a solution to a very similar example.
Please show your work below.
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Normal
Enter your answer here
√x
E BIUS X₁ X²
22 Ix
Practice.
A JA
The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
What is the Equation of line?
The equation of the line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
we have given that;
After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Now,
Since, After 13 minutes, the airplane has 32,882 gallons of fuel. After 31 minutes, the airplane has 34,902.5 gallons of fuel.
Hence, The equation of line passes through the points (13, 32882) and (31, 34902.5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (32882 - 34902.5) / ((31 - 13)
m = 2020.5 / 18
m = 112.25
Thus, The equation of the line with slope 112.25 is,
⇒ y - 32885 = 112.25 (x - 13)
⇒ y - 32885 = 112.25x - 1459.25
⇒ y = 112.25x - 1459.25 + 32885
⇒ y = 112.25x + 31.425.75
Therefore, The function in f(t) form that describes the amount of fuel in the plane at time t will be:
f(t) = 112.25t + 31.425.75
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Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)=(x²-64)^{1/11} on the domain [-8,9]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The absolute maximum is , which occurs at x= (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.)
B. There is no absolute maximum.
The critical points for the equation [tex]f(x)=(x^{2} +64)^{\frac{1}{11} }[/tex] is
[tex](x,f(x))[/tex] = [tex](0,2^{\frac{6}{11} })[/tex] = [tex](0,1.46)[/tex]. at x=0
The absolute maximum is at [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex], at x=9.
What is the absolute maximum of an equation?
The highest conceivable values for f are represented by the absolute maximum (sometimes called the global maximum) of a function f(x) (x). Let's imagine the function's critical value, x=c, is present within its domain. If the inequality f(c) [tex]\geq[/tex] f(x), x is a domain, then the function f(x) is said to satisfy an absolute maximum when x=c.
To find the critical points, we find the value of f'(x) and equate to 0.
[tex]\frac{d}{dx} (\sqrt[11]{x^{2}+64} )=0[/tex]
we get x=0.
We see that f'(x) exists for all x between [-8,9].
We also find the endpoints, that is -8 and 9.
Then we calculate f(x) at critical points and endpoints.
We calculate f(x) at 0, -8, and 9.
We get,
for x=0, f(x)= [tex]2^{\frac{6}{11} }[/tex]
for x=-8, f(x)= [tex]2^{\frac{7}{11} }[/tex]
for x=9, f(x)= [tex]\sqrt[11]{145}[/tex]
We see that the value is maximum at x=9, and f(x) becomes [tex]\sqrt[11]{145}[/tex].
Hence we get the absolute maximum is [tex](x,f(x))\\[/tex] = [tex](9,\sqrt[11]{145} )[/tex] = [tex](9,1.6)[/tex]
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What is Q(1.5) if ()=cos() f(x)=cos(x) and Q(x) is centered at /2? Round your answer to 4 decimals, for example, 0.1234.
Step-by-step explanation:
Hello. Can you repost the question and just for clarification is this Taylor, Maclaurin Series?
Sterling has prepared the following two-column proof below. He is given that ∠OLN ≅ ∠LNO and he is trying to prove that OL ≅ ON. Triangle OLN, where angle OLN is congruent to angle LNO Step Statement Reason 1 ∠OLN ≅ ∠LNO Given 2 Draw OE as a perpendicular bisector to LN by Construction 3 m∠LEO = 90° Definition of a Perpendicular Bisector 4 m∠NEO = 90° Definition of a Perpendicular Bisector 5 LE ≅ EN Definition of a Perpendicular Bisector 6 ΔOLE ≅ ΔONE Hypotenuse-Leg (HL) Postulate 7 ∠LEO ≅ ∠NEO Transitive Property of Equality 8 OL ≅ ON CPCTC Sterling made two errors in the proof. Identify and correct the errors. Question 5 options:
The two errors that Sterling made in the proof include:
The step 2 must be that statement OE is the perpendicular bisector to LN.The step 6 statement that OL is identical to ON is not necessarily in the proof.What are the error made?In this case, it should be noted that the step 6. statement must be that LEO is equal to NEO. This is due to the substitution property of equality.
The substitution property of equality states that one value can be substituted for another in an expression or equation and the result will be the same. If the values of x and y are equal, then x and y can be substituted for one another.
Also, the step 7 should be that OLE is identical to ONE. The reason is due to the angle-side-angle postulate. According to the AAS Postulate, if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another, the triangles are congruent.
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there is a line that includes the point 9,7 and has a slope of 1. what is its equation in slope intercept form?
Step-by-step explanation:
Note that the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Plug in the slope for m and the given coordinate for x and y:
9 = (7)(2) + b
9 = 14 + b
b = -5
y = 7x - 5
Morris Company applies overhead based on direct labor costs. For the current year, Morris Company estimated total overhead costs to be $408,000, and direct labor costs to be $2,040,000. Actual overhead costs for the year totaled $386,000, and actual direct labor costs totaled $1,820,000. At year-end, Factory Overhead is:
At year-end, Factory Overhead is debit of $34000.
What is profit and loss?
A profit and loss (P&L) statement could be a monetary report that has a outline of a company’s revenue, expenses and profit. It provides investors and alternative interested parties an insight into however an organization is working and whether or not it's the flexibility to get a profit.
Main Body:
Estimated total overhead costs = $456,000
Estimated direct labor costs = $2,280,000
Actual overhead costs= $422,000
Actual direct labor costs= $1,940,000
To calculate the factory overhead, we need to first calculate Estimated overhead rate.
Estimated overhead rate = Estimated total overhead costs / Estimated direct labor costs
= $456,000 / $2,280,000
= 0.2
= 20%
Therefore;
Actual Factory overhead = Actual direct labor cost × application rate
= $1,940,000 × 20%
= $388,000
We can get the balance in the overhead account as shown below;
Balance = Actual overhead cost - Actual cost that should be applied
= $422,000 - $388,000
= $34,000 (Debit).
Hence there is debit of $34000.
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I need help
Arc QR =
Arc RS=
QPS =
PSR =
SRQ =
Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:
Arc QR = 48°
Arc RS = 96°
Arc QPS = 216°
Arc PSR = 186°
Arc SRQ = 144°
What is the Inscribed Angle Theorem?The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.
Find arc PSR:
Arc PSR = 2(93) [based on the inscribed angle theorem]
Arc PSR = 186°
Find arc QR:
Arc QR = 360 - arc PQ - arc PSR
Substitute
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
Arc QPS = 126 + 90
Arc QPS = 216°
Arc PSR = arc PS + arc RS
Arc PSR = 90 + 96
Arc PSR = 186°
Arc SRQ = arc RS + arc QR
Arc SRQ = 96 + 48
Arc SRQ = 144°
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Answer: 48 96
Step-by-step explanation:
Arc QR = 360 - 126 - 186
Arc QR = 48°
Arc RS = arc PSR - arc PS
Arc RS = 186 - 90
Arc RS = 96°
to serve one person at a local restaurant it takes 10 minutes to serve pot five people it takes 18 minutes right and solve an equation to find the number of minutes it will take to serve a party of eight
By finding an evaluating a linear equation we will see that it takes 24 minutes to serve a group of 8 people.
How long takes to serve a party of eight?
Let's assume that the relation between the number of people and the time it takes to serve them is linear.
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
a = (y2 - y1)/(x2 - x1)
Here we have two points:
1 person, 10 minutes, written as (1, 10)
5 people, 18 minutes, written as (5, 18)
Then the slope is:
a = (18 - 10)/(5 - 1)
a = 8/4 = 2
Then the linear equation is:
y = 2x + b
To find the value of b, we can replace the values of one of the points, I will use (1, 10) so we will get:
10 = 2*1 +b
10 = 2 + b
10 - 2 = b
8 = b
The linear equation is:
y = 2x + 8
For 8 customers, the time will be:
y = 2*8 + 8
y = 24
It will take 24 minutes to serve 8 people.
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(a) Complete the statements below about the graphs of y=-1/3 x and y=x .
Compared to the graph of y=x , the graph of y=-1/3 x is
Compared to the graph of y=x , the graph of y=1/3x intersects the y -axis at
The correct statements regarding the functions are given as follows:
a)
Compared to the graph of y = x, the graph of y = -1/3x is vertically compressed by a factor of 3 and reflected over the x-axis.Compared to the graph of y = x, the graph of y = -1/3x intersects the y-axis at the same place, which is the origin.b)
Compared to the graph of y = x, the graph of y = x - 2 is shifted right two units.Compared to the graph of y = x, the graph of y = x - 2 intersects the y-axis two units below.What are the transformations to the functionFor item a, the functions are given as follows:
y = x.y = -1/3x.The multiplication by -1/3 means that the vertically compressed by a factor of 3 and reflected over the x-axis, due to the multiplication by the negative number.
For item b, the functions are given as follows:
y = x.y = x - 2.The transformation is:
x -> x - 2, meaning that the function was shifted right two units.
The intersection with the y-axis is at the value of y when x = 0.
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Solving distance, rate time problem
A total of 396 miles and 2.2 hours will pass between the two trains on the Long.
How to calculated the Distance and rate time?For additional information on how to handle rate-time-distance or motion problems, scroll down the page.
Moving away from one another are the two trains.
85x + 95x = 396
To solve you combine like terms. The like terms are 85x and 95x
85x + 95x = 180x
Right now, you
180x = 396
Now multiply by 180.
180 divided by 396 equals 2.2.
X= 2.2
That's how you do things, in my opinion.
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There were 202 tickets sold during the first hour of sales for the opening match of the
World Cup. Tickets for the cheap seats cost $50, and the best seats cost $556. Use algebra
to find out how many tickets of each type were sold if the total receipt was $42,990,
Answer:
137 cheap tickets sold, and 65 best seats sold
Step-by-step explanation:
x+y=202
50x+556y=42900
x=202-y
50(202-y)+556y=42900
10100-50y+556y=42900
10100+506y=42900
506y=32890
y=65
x=202-65
x=137
x= Cheap tickets, y= expensive tickets
If A and B are independent events with P(A)=0.5 and P(B)=0.1, find P(A AND B).
The probability of event A and event B of the independent events will be 0.05.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the conditional probability is given as,
P(A and B) = P(A) x P(B)
Event A and event B are independent events. The probability of event A is 0.50 and the probability of event B is 0.10.
Then the probability of event A and event B of the independent events is given as,
P(A and B) = P(A) x P(B)
P(A and B) = 0.50 x 0.10
P(A and B) = 0.05
The probability of event A and event B of the independent events will be 0.05.
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Zeno jumped 8 meters. Then he jumped half as far again (4 meters). Then he jumped half as far again ( 2 meters). So after 3 jumps, he was 8+4+2=14 meters from his starting place.
a) Zeno kept jumping half as far again. How far would he be after 4 jumps? 5 jumps? 6 jumps?
b) Before he started jumping, Zeno put a mark on the floor that was exactly 16 meters from his starting place. How close can Zeno get to the mark if he keeps jumping half as far again?
a) His distances after each jump are given as follows:
4 jumps: 15 meters.5 jumps: 15.5 meters.6 jumps: 15.75 meters.b) He will jump exactly 16 meters.
What is a geometric sequence?In a geometric sequence, each term is obtained by the multiplication of the previous term by the common ratio.
In this problem, the sequence is given as follows:
8, 4, 2, ...
The common ratio is of:
q = 2/4 = 4/8 = 0.5.
Then the next jumps are given as follows:
4th jump: 2 x 0.5 = 1 meter -> 14 + 1 = 15.5th jump: 2 x 1 = 0.5 meters -> 15 + 0.5 = 15.5.6th jump: 2 x 05 = 0.25 meters -> 15.5 + 0.25 = 15.75.The sum of the elements of an infinite geometric sequence is given as follows:
[tex]S = \frac{a_1}{1 - q}[/tex]
In which [tex]a_1[/tex] is the first element.
Hence for this problem, the sum is of:
S = 8/(1 - 0.5) = 16 meters.
Which means that he will reach exactly the desired distance.
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Given dy/dt=2y and y(2)=200. Find y(7).
The required value of y(7) is given as y (7)= 4412711.8.
Given that,
Given dy/dt=2y and y(2)=200.
The action of bringing concurrently shorter components into a single system that acts as one is known as integration.
Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8
Thus, the required value of y(7) is given as y (7)= 4412711.8.
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at the Mayfair Stella, Mary, cris, Elli won 60 prizes altougheter. Mary won one third of them, Stella won one fifth of them, and illli got one fourth of the total. how many prizes did chris win
The number of prizes that Chris won out of 60 will be 13.
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.
At the Mayfair Stella, Mary, Cris, and Elli won 60 awards altogether. Mary won 1/3 of them, Stella won 1/5 of them, and Elli got 1/4 of the aggregate.
Then the number of prizes that Chris won is given as,
⇒ 60 - 60 / 3 - 60 / 5 - 60 / 4
⇒ 60 - 20 - 12 - 15
⇒ 60 - 47
⇒ 13
The number of prizes that Chris won out of 60 will be 13.
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let be an matrix and an matrix so that the product is defined. suppose we know that the rref of both a and b have pivots in every column. explain why it follows that every column of rref(a b) also has a pivot in each column.
A pivot in every row means that the linear system A x=b has at least one solution, for every b.
If every column has a pivot, then the linear system A x=b has at most one solution.
If both hold (which can happen only if A is a square matrix), we get that the system A x=b has unique solution for every b.
A pivot in every row is equivalent to A having a right inverse, and equivalent to the columns of A spanning
[tex]$\mathbb{R}^m$ ( $m$[/tex] is the number of rows).
A pivot in every column is equivalent to A having a left inverse, and equivalent to the columns of A being linearly independent
A pivot means fundamentally changing the direction of a business when you realize the current products or services aren't meeting the needs of the market. The main goal of a pivot is to help a company improve revenue or survive in the market, but the way you pivot your business can make all the difference.
The first nonzero item of each row in a matrix in row-echelon form is known as a pivot, and the columns in which pivots appear are known as pivot columns.
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