The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.
What ordered pair is a solution to the system of linear equations?
An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,
a₁ x + b₁ y = c₁
a₂ x + b₂ y = c₂
A solution to a linear system is an ordered pair (x ,y) that solves both the equations .
To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.
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a boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6 mi from a restaurant on the shore (see figure). a woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. if she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time? if she walks at 3 mi/hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)?
(a) she land to minimize the total travel time is 2.4min
(b) the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6
(a)
T(x) = time rowing + time walking
= [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex] +[tex]\frac{6 - x}{3}[/tex]
T(x) = 1/2[tex]\sqrt{(x^{2} + 16)}[/tex] + 2 - [tex]\frac{x}{3}[/tex]
first derivation
T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x - 1/3
= [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] - 1/3
T'(x) = 3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex]
T'(x) = 0
3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] / 6[tex]\sqrt{(x^{2} + 16)}[/tex] = 0
3x - 2 [tex]\sqrt{(x^{2} + 16)}[/tex] =0
3x/2 = [tex]\sqrt{(x^{2} + 16)}[/tex]
9[tex]x^{2}[/tex]/4 = [tex]x^{2}[/tex] + 16
9[tex]x^{2}[/tex] = 4 [tex]x^{2}[/tex] + 64
5 [tex]x^{2}[/tex] = 64
[tex]x^{2}[/tex] =64/5
x = [tex]\sqrt{64/5}[/tex]
x = 8/[tex]\sqrt{5}[/tex]
x = 8[tex]\sqrt{5}[/tex]/5
total travel time = 6 - 8[tex]\sqrt{5}[/tex]/5 = 2.4 min
she land to minimize the total travel time is 2.4min
(b) T(x) = time rowing
= [tex]\frac{\sqrt{x^{2} +16} }{2}[/tex]
first derivation
T'(x) = 1/4[tex]\sqrt[-1/2]{(x^{2} + 16)}[/tex] .2x
= [tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex]
T'(x) = 0
[tex]\frac{x}{2\sqrt{(x^{2} + 16)} }[/tex] =0
x = 0
minimum speed = 6-x = 6-0=6
the minimum speed at which she must row so that the quickest way to the restaurant is to row directly is 6
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Use the distance formula to find the distance, to the nearest tenth, from R(7, -2) to
W(-2, 3).
The distance between (7,-2) and (-2,3) is 11.2 units using the distance formula.
What is distance formula?Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage. a measurement of the distance between two points along a line or line segment. It's formula is "distance formula=√(x2-x1)²+(y2-y1)²".
Here,
distance formula=√(x2-x1)²+(y2-y1)²
=√(-2-7)²+(3--2)²
=√(-9)²+5²
=√81+45
=√126
=11.225 units
rounding to nearest tenth,
=11.2 units
Using the distance formula, the distance between (7,-2) and (-2,3) is 11.2 units.
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reyshel has to carry 20 pounds of clothes everyday 1 pound is about 453.6 grams about how many grams does reyshel have to carry in a day
Answer:9072
Step-by-step explanation:
453.6 x 20 = 9072
4(3/2 - 3x) Use the distributive property to remove the parentheses.
Simplify your answer as much as possible.
Answer:
[tex]-12x+6[/tex]
Step-by-step explanation:
Take a look at the attachment,,,
Hope this helps! :)
Answer:
[tex]6 + 12x[/tex]
Step-by-step explanation:
The distributive property states that A(B + C) = AB + AC.
Therefore,
[tex]4 \left( \dfrac{3}{2} - 3x \right) = 4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]
Now we can simplify each term:
[tex]4 \left( \dfrac{3}{2} \right) + 4(3x)[/tex]
[tex]= \dfrac{12}{2} + 12x[/tex]
[tex]= 6 + 12x[/tex]
Mark is reading a new book for his Literature class. The book has a total of 160 pages. Mark’s goal is to complete of the book by the end of the week. If Mark has read 24 pages so far, what fraction of the 1/4 book does Mark have left to read by the end of the week in order to reach his goal?
The fraction left for Mark to read is 17/20.
How to calculate the fraction?From the information illustrated, he wants to complete of the 160 pages book by the end of the week and Mark has read 24 pages so far.
The number of pages left will be:
= 160 - 24
= 136 pages
Therefore, the fraction of pages left will be:
= Number of pages left / Total pages
= 136 / 160
= 17/20
The fraction is 17/20.
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What is the expansion of the series "sum from n equals 1 to 4 of 3 to the n plus 1 power question mark" (photo includes proper equation)
9 + 27 + 81 + 243
9 + 12 + 15 + 18
3 + 9 + 27 + 81
3 + 6 + 9 + 12
The expansion of the series ⁴∑ₙ = ₁ 3ⁿ ⁺ ¹ is; 9 + 27 + 81 + 243
How to expand series?We are given the summation formula of the series as;
⁴∑ₙ = ₁ 3ⁿ ⁺ ¹
At n = 1, we will input 1 for n and we have;
3¹ ⁺ ¹ = 3² = 9
At n = 2, we will input 2 for n and we have;
3² ⁺ ¹ = 3³ = 27
At n = 3, we will input 3 for n to get;
3³ ⁺ ¹ = 3⁴ = 81
At n = 4;
3⁴ ⁺ ¹ = 3⁵ = 243
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The following list shows the number of goals scored by a soccer team in each of 9 games.
0, 0, 1, 1, 1, 3, 3, 4, 5
How does the median number of goals scored compare with the mean number of goals scored?
answer choices:
The median is equal to the mean
The median is less than the mean by 1.
The median is greater than the mean by 1.
The median is less than the mean by 2.
The median for a particular set is one less than the mean.
Given;
List of order for goals scored by a soccer team in 9 matches
= 0, 0, 1, 1, 1, 3, 3, 4, 5
To find the relation between mean and median;
The obtained mean = Sum of observations/number of observations
= 0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5
= 18/9
= 2
Mean = 2
For median;
let us write the given observations in ascending order;
⇒ 0, 0, 1, 1, 1, 3, 3, 4, 5
Here no. of observations is r = 9 which is an odd number.
Therefore observation at 5th is a middle position which has 1 as a value.
Median = 1
Therefore, the median is less than the mean by 1.
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Find the value of *p* using Cos. Answer with explanation and I will give brainlist.
Answer:
The angle is approximately 111.199 degrees.
Step-by-step explanation:
Cosine is adjacent over hypotenuse.
The hypotenuse is the longest side of the triangle.
In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.
In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.
Plugging in the numbers:
[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]
Find the value of X that makes lines u and v parallel 7-12
The value of x that makes lines u and v parallel is 6. Option A is correct.
First, let us understand the angles formed by parallel and transversal lines:
The different types of angles are alternate exterior angles, alternate interior angles, corresponding angles, consecutive angles, etc.
From the picture attached,
If the lines u and v are parallel and a third line (transversal) is intersecting these lines at two distinct points,
Both the angles given in the picture will be equal in measure as these angles are alternate exterior angles if u and v are parallel.
20x + 10 = 130 degrees
20x = 130 - 10 degrees
x = 120 / 20 = 6
So, the value of x is 6.
Thus, the value of x that makes lines u and v parallel is 6. Option A is correct.
For question please check the below figure:
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Please help!! assignment due for tomorrow, will mark brainliest for correct answer!! Need ASAP
The object moves at a speed of 25.352 m/s
Subject of FormulaThe subject of a formula is the variable that is being worked out. It can be recognized as the letter on its own on one side of the equals sign. It is a variable which is expressed in terms of other variables involved in the formula.
Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.
In the question given, we have an equation;
s = d/t
d = 180m, t = 7.1s
s = 180 / 7.1
s = 25.352 m/s
The speed (s) of the object is 25.352 m/s
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the graph of a linear function is shown . which word describes the slope of the line
Answer:
positive
Step-by-step explanation:
Help my with this problem please 20 points
The difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12 is -[tex]4x^2[/tex] - 4x 20
The first polynomial is given that
[tex]2x^2[/tex] - 9x + 8
The second polynomial is
[tex]6x^2[/tex] - 5x - 12
Here we have to find the difference, to find that we need to subtract the second polynomial from the second polynomial
Then,
[tex]2x^2[/tex] - 9x + 8 - ( [tex]6x^2[/tex] - 5x - 12 )
Open the bracket using the distributive property
[tex]2x^2[/tex] - 9x + 8 - [tex]6x^2[/tex] + 5x +12
Combine the like terms
[tex]2x^2[/tex] - [tex]6x^2[/tex] -9x +5x + 8 +12
Apply the arithmetic operations on like terms
-[tex]4x^2[/tex] - 4x 20
Hence, the difference of the polynomials [tex]2x^2[/tex] - 9x + 8 and [tex]6x^2[/tex] - 5x - 12 is -[tex]4x^2[/tex] - 4x 20
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Can someone pls give me the answer to that?
The values of x and y which are the missing terms of the given triangle have their values as; x = ⁵/₂ and y = ⁹/₄
How to Interpret Division of line segments?
From the given triangle, we can see that the transverse line intersects both side lengths at their midpoints. Thus, we can say that;
3x - 4 = x + 1 ------(1)
⁴/₃y + 2 = 4y - 4 ------(2)
Let us solve equation 1 by rearranging to get;
3x - x = 1 + 4
2x = 5
x = ⁵/₂
Similarly, we can say that for equation 2;
4y - ⁴/₃y = 2 + 4
4y - ⁴/₃y = 6
Multiply through by 3 to get;
12y - 4y = 18
8y = 18
y = 18/8
y = ⁹/₄
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Here are the first six terms of an arithmetic sequence.
1
7 13 19 25 31
a) Find an expression, in terms of n, for the nth term of this sequence.
The nth term of a different sequence is 5n²
b) Work out the 4th term of this sequence. 4th term =
(a) The expression of nth term of arithmetic sequence is [tex]a_n=1+(n-1)6[/tex] and (b) 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
What is arithmetic sequence?
It is a sequence of numbers which have same difference between two consecutive numbers. The common difference can be any positive number or negative number or even it can be 0.
The six terms of the arithmetic sequence are as follows:
1,7,13,19,25,31
Calculate the common difference as follows:
7-1=6
13-7=6
19-13=6
Since it is an arithmetic sequence hence common difference is 6.
Hence, [tex]d=6[/tex].
Now, substitute value of the first term and the common difference in the following expression of the nth term.
[tex]a_n=a+(n-1)d\\a_n=1+(n-1)6[/tex]
Now, the nth term of another sequence is as follows:
[tex]a_n=5n^2\\[/tex]
Substitute n=4 in the above equation.
[tex]a_4=5(4)^2\\=80[/tex]
Hence, (a) the expression of nth term is [tex]a_n=1+(n-1)6[/tex] and 4th term of the series [tex]a_n=5n^2\\[/tex] is 80.
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Can someone please help me
From the given data
a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks
b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km
In the graph,
The x axis represents the Time since start in minutes and the y axis represents the distance from the start in kilometers.
In x axis each block represents 5 minutes
The maximum value of time taken in table = 35 minutes
Then the number of squares wide does the grid need to be so that the data fits on the graph = 35 / 5
= 7 blocks
Part b
If the grid is 20 squares tall
The maximum value of distance = 1.8 km
Then the value of A will be
1.8 / 20 = 0.09 km
Hence, from the given data
a) Then the number of squares wide does the grid need to be so that the data fits on the graph is 7 blocks
b) If the grid is 20 squares tall, then the variable A can be replaced by 0.09 km
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Vanya gathered some mushrooms. He dried 2/5 of them. Then he pickled 5/9 of the remaining mushrooms and fried 28 that were left. How many mushrooms did he gather.
Need this stat this is due tomorrow
Answer:
105
Step-by-step explanation:
1. x = mushroom he gather
2. he dry 2/5 from he gather, 2/5 from x
3. he pickled 5/9 of remaining mushroom
find the remaining mushroom value first, x-2/5x = 3/5x
then multiply with 5/9, 5/9(3/5x) = 15/45x
4. total mushroom - dry - pickled, he still have 28 to fry
5. write the equation like this
x - 2/5x - 15/45x = 28
45/45x - 18/45x -15/45x = 28
12/45x = 28
x = 28(45) / 12
x = 105
Nick’s youth group has 20 regular students that attend weekly get togethers. They saved up enough money for each person to go swimming 15 times each with the daily pay plan. After they saved that amount, they found out they can use the early pay plan and save money. They plan to donate their savings to the church since it’s in need of a new sound system. How much money will they be able to donate with the savings from all 20 youth? (Please show all your work for full credit)
The money that the group will be able to donate with the savings from all 20 youth is $1400.
What is the amount?Let the daily pay plan for each youth = y.
Daily pay plan for 20 youths = 20y
Weekly pay plan = 7 × 20y = 140y
Assuming each youth saves $10 daily
Daily savings for 20 youth:
= 20 × $10
= $200
Weekly savings for 20 youth:
= 7 × $200
= $1400
If they used the early pay plan 140y to go swimming, they saved $1400 which they donated to the church.
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A train journey started at 17 50 and finished at 02 25 the next day.
How long did the train journey take?
Give your answer in hours and minutes
Answer:
8 hours and 35 minutes. (8:35)
Step-by-step explanation:
8 hours and 35 minutes.
515 minutes.
i really need help with this
look at points c and d on the graph what is the distance in units between points c and d round to nearest hundredth
Answer:
7.07
Step-by-step explanation:
Draw a horizonal line and a vertical line to creat a right triangle. The horizontal measurement would be 5 and so would the horizontal measurement.
Use the Pythagorean theorem
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] The c side is the length that you are looking for
[tex]5^{2}[/tex] + [tex]5^{2}[/tex] = [tex]c^{2}[/tex]
25 + 25 = [tex]c^{2}[/tex]
50 = [tex]c^{2}[/tex]
[tex]\sqrt{50}[/tex] = [tex]\sqrt{c^{2} }[/tex]
7.07 = c Rounded to the nearest hundredths
2
Determine the volume of the rectangular
prism, if each cube represents 1 unit.
The volume of the rectangular prism is 12 cubic inches
It is given that Each cube represent 1 unit
The base length of the rectangular prism = 4 inches
The base width of the rectangular prism = 3 inches
The height of the rectangular prism = 1 inches
The volume of the rectangular prism = The base length of the rectangular prism × The base width of the rectangular prism × The height of the rectangular prism
Substitute the values in the equation
The volume of the rectangular prism = 4 × 3 × 1
= 12 cubic inches
Hence, the volume of the rectangular prism is 12 cubic inches
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Given N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1). Find a such that NO || PQ.
The value of x is -8.
1).
N(-6,-8), O(5, 3), P(0, 9), and Q(x, 1).
slope between NO = y2 - y1 / x2 - x1
= 3 - (-8) / 5 - (-6)
= 3+8 / 5+6
= 11/11
= 1
slope between PQ = 1-9 / x-0
= -8/x.
Given lines are parallel so there slopes are equal
1 = -8/x
x = -8.
Therefore the value of x is -8.
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What is the solution to the system of equations graphed below?
the answer for your question above is (-1,-1) or you could say option no.3
What is the equation of the line in slope-intercept form?
Answer:
y= [tex]\frac{5}{2}[/tex]X +5
Step-by-step explanation:
for a fixed location, the number of sunlight hours in a day fluctuates throughout the year. suppose that the number of daily sunlight hours in a particular location can be modeled by the following. l(t)
On October 24, 218 days after March 20, there will be 10 hours of sunlight.
The number of daily sunlight hours of a particular location is modelled by the trigonometric equation,
l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
Here , L(t)= Number of sunlight hours in a day.
t = Number of days after 20th March .
Now we are required to determime the day during first 365 on which there are 10 sunlight hours ,that is, we need the value of "t" for which L(t) =10 hours. So in the given equation by putting L(t)= 10 and solving for t , follows as,
l(t) = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
10 = 12 + 3.5sin (2[tex]\pi[/tex]/365t)
10-12 = 3.5sin (2[tex]\pi[/tex]/365t)
-2 = 3.5sin (2[tex]\pi[/tex]/365t)
-2/3.5 = sin (2[tex]\pi[/tex]/365t)
-0.574 = sin (2[tex]\pi[/tex]/365t)
For the inverse function of y = sin x
sin ⁻¹(y) =x + 2n[tex]\pi[/tex]
Now as we are required to calculate the day having 10 sunlight hours in first 365 days so putting n=0 we get,
t = -35.3521 or t =217.9422
Now t can not be negative as we want to find the day after march 20 having 10 sunlight hours. So neglecting t=-35.3521 . Now we get t=217.9422 .
Rounding off we get ,t=218 which is the required answer.
Hence, 218 days after march 20 i.e on October 24 it will have 10 sunlights.
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Which function includes all the ordered pairs in the table
The function that includes all the ordered pairs in the given table is y = -x - 4
First choose two points
First point = (0, -4)
Second point = (2, -6)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values in the equation
The slope of the line = (-6 - (-4) / (2 - 0)
= -6 + 4 / 2
= -2 / 2
= -1
Here at X = 0, the value of Y = -4
Therefore the y intercept of the line = -4
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Substitute the values in the slope intercept form
y = -1x - 4
y = -x - 4
Hence, The function that includes all the ordered pairs in the given table is y = -x - 4
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Tamara Was worried about the six-year-old dog. Suze, so she took her to three different
veterinarians. Each vet told her the approximate age o her dog in dog years based on Suze's health. Tamara graphed her dog's age in dog years and included the three vet approximations at age 6. Do you think this graph is a function? Why or why not?
Answer:
yes
Step-by-step explanation:
every x value has at least one y value
Simplify: (3x+4) - (x+2)
Answer:
[tex] \sf \: 2x + 2[/tex]
Step-by-step explanation:
Given expression,
→ (3x + 4) - (x + 2)
Let's simplify the expression,
→ (3x + 4) - (x + 2)
→ 3x + 4 - x - 2
→ (3x - x) + (4 - 2)
→ (2x) + (2)
→ 2x + 2
Hence, the answer is 2x + 2.
a) Factorise 3x²+ 13x10
Answer:
(3x+10)(x+1)
Step-by-step explanation:
This is the answer for 3x^2+13x+10.
I think you made an error while typing.
Hope this helps!
10x+5y=5x+20 solve for y
The value of y in the expression is y= - (x + 4) or, y= (x -4)
ExpressionAlgebraic expression in mathematics is a phrase that include coefficients, unknown variables operations, and constants
To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;
Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation
5y =5x -10x+20
Step 2: Evaluate the the expression 5y =5x -10x+20
5y = -5x + 20
Step 3: Divide both sides by 5
[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]
y = -5x/5 + 20/5
y = - (x + 4) or, y= (x -4)
Therefore, the value of y in the expression is y= - (x + 4) or, y= (x -4)
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