solve the system of equations x = 17 - 4 y = x - 2
Answer:
To solve the given system of equations, we can start by substituting the value of x in the second equation into the first equation. Since the second equation tells us that x = y - 2, we can substitute y - 2 for x in the first equation to get:
x = 17 - 4y
y - 2 = 17 - 4y
Then, we can combine like terms on the right-hand side to get:
x = 17 - 4y
-3y = 15
Finally, we can divide both sides by -3 to solve for y, and then substitute this value back into one of the original equations to solve for x:
x = 17 - 4y
y = -5
x = 17 - 4(-5) = 17 + 20 = 37
Therefore, the solution to the system of equations is x = 37 and y = -5.
3
Gerry and Claire have been out walking using a map with a scale of 2 cm: 1 km.
The distance they have walked on the map is 14 cm.
How far have they actually walked?
Answer:
7 km
Step-by-step explanation:
14/2 cm which equals 7km
How many different ID cards can be made if there are seven digits on a card and no digit can be used more than once? What if digits can be repeated?
The number of ID cards when no digit can be used more than once is 604,800 and when the digits can be repeated it will be 10,000,000 ID cards.
What is Permutations?Permutations are several ways to arrange things in a specific sequence. It can alternatively be stated as the linear reordering of items within an ordered set.
As per the given information in the question,
Let's first make a list of all the potential outcomes. As follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
a.
No numeral may be used multiple times in the first instance.
Therefore,
10 × 9 × 8 × 7 × 6 × 5 × 4
= 604,800 ID cards
b.
In the second scenario, assuming it is possible to repeat the digits, then,
10 × 10 × 10 × 10 × 10 × 10 × 10 = 10,000,000 ID cards.
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Player First
Round Final
Round
Golfer 11 72 72
Golfer 12 72 70
Golfer 13 70 73
Golfer 14 70 77
Golfer 15 68 70
Golfer 16 68 66
Golfer 17 71 70
Golfer 18 70 68
Golfer 19 69 68
Golfer 20 67 71
Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?
(a) Use α = 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use μd = mean score first round − mean score fourth round.
Calculate the value of the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
(b) What is the point estimate of the difference between the two population means? (Use mean score first round − mean score fourth round.)
The point estimate of the difference between the two population means is -1.05.
Here, we are given the data representing the scores of the golf players in the 1st and final rounds.
a. The significance level is: α = 0.10
we can construct the following hypothesis test-
Null hypothesis H₀ ⇒ μd = 0
This implies that there is no difference between the population mean of the first round and final round.
Alternative hypothesis: Ha ⇒ μd ≠ 0
This implies that there is a difference between the population mean of the 1st round and final round.
Now, the test statistic will be-
[tex]t = (d-mean_{d})\sqrt{n}/ s_{d\\}[/tex]
we can use excel to calculate the test statistic.
This will give us: 0.10 < P < 0.20
b. the main margin of error is 90% confidence level. This means that there is no significant difference, hence - 1.05.
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Your question was incomplete. Check for the missing figure below.
Write the standard form of the equation of the line that passes through the points (-3,-2) and (-1,0).
A) x + y = 0
C) x + y = 2
B) x - y = 0
D) x - y = -1
In standard form the equation of the line passing through the points,
(-3, -2) and (-1, 0). is
x - y = -1
How to determine the equation of the line passing through the given pointsInformation given in the question include
points, (-3, -2) and (-1, 0).
Standard form of linear equations is of the form Ax + By = C
The slope is represented as m, The slope by definition is the ratio change of the output values to the input values
the slope, m calculating using the points (-3, -2) and (-1, 0).
m = (0 - (-2)) / (-1 - (-3))
m = (2) / (2)
m = 1
if the line passes through point X(-1, 0)
y - 0 = 1(x - (-1))
y = x + 1
x - y = -1
the intercept C = 1
The equation of the line is x - y = -1
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the formula for the area of a triangle is A=1/2bh. find the area of a triangle with a base (b) of 8 feet and a height (h) of 11 feet. the area of the triangle is_ spuare feet.
Answer: 44ft^2
Step-by-step explanation:
plug it into the equation, h=11, b=8
so A=1/2(11)(8) = 44ft^2
a satellite traveling in a circular orbit 1,000 miles above the earth passes directly over a tracking station at noon. assume that the satellite takes 2 hours to make an orbit and that the radius of the earth is 4,000 miles. find the distance between the satellite and tracking station at 12:03 p.m. draw a picture (using the idea of orbits like above), then solve.
The distance between the satellite and the tracking station is 1220 miles
To find the distance between the satellite and the tracking station we need to apply cosine law:
[tex]c^{2} =a^{2} +b^{2} -2ab cos(\beta )----------(1)[/tex]
where:
c=length of side c
a=length of side a
b=length of side b
β=angle opposite c
we need to find the angle of β
computing the angle β gives
[tex]\beta =\frac{3min}{120min} *360[/tex]
β=9°
Now substitute the β value ,a=4000,b=5000,in cosine law, and we get
[tex]x^{2} =4000^{2} +5000^{2} -2(4000)(5000)cos 9[/tex]
[tex]=(16+15-39.51)*10^{6 }\\=1.49*10^{6}[/tex]
x=1.22x10^3
x=1220 miles distance from the satellite to the tracking station.
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14) The sum of the digits of a two digit number is 12. The number obtained by reversing the digits is 18 less than the original number. What is the original number? Solve by using a system of equations. Write the 2 equations in the space provided. Show all work, including the method of your choice, used to solve.
Equation 1:
Equation 2:
The original number is 57.
The two equations are x+y = 12 and (10y+x)−(10x+y) = 18.
Let the digit at the tens place be x and the digit at the unit place be y.
x+y = 12 .........(1)
Required Number = (10x+y).
Number obtained on reversing the digits = (10y+x).
According to the condition, we get
(10y+x)−(10x+y) = 18
→ 9y−9x = 18
→ y−x = 2 ..........(2)
Adding (1) and (2), we get
2y = 14
y =7
x = 12 - 7
x = 5
Hence, the required number is 57.
The equations used to solve this is x+y = 12 and (10y+x)−(10x+y) = 18.
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based on the text, what is the meaning of collinear? responses a unconnected to any sort of lineunconnected to any sort of line b equally distant in every directionequally distant in every direction c lying on or passing through the same linelying on or passing through the same line d connected sections along a curved lineconnected sections along a curved line
On solving the provided question, we can that the answer - The distance between two points is the length of a line segment that connects them.
What is straight lines?A line is a shape that has no width, depth, or curve in its geometry. It is an item that can be used for a long time. A line can exist in a two-dimensional, three-dimensional, or more dimensional space, but is still a one-dimensional object. A line segment with two endpoints is commonly called a "line".
Main notations:
A plane is a flat, indefinitely long, 2D surface with no thickness. Option 1 is accurate. A point is a precise place. It just has position; it has no length, breadth, or depth. Option 2 is untrue. Collinear points are any two or more points that are situated differently yet are on the same line. Option 3 is untrue. A line has no thickness, is straight (has no bends), and goes in both directions without ending (infinitely). Option 4 is accurate. The length of a line segment that links two places represents their distance. Option 5 is accurate.
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A bag of marbles contained 40 blue marbles and 46 white marbles (and no other marbles). For a game, marbles of each color were chosen from the bag. Of the 40 blue marbles,3/5 were chosen.
Use this information to answer the questions below.
If not enough information is given to answer a question, click on "Not enough information."
(a) How many of the bag's marbles were not chosen?
(b) How many marbles were in the bag before the game?
(c) How many of the bag's blue marbles were chosen?
Number of marbles were not chosen = 62 marbles
Number of marbles were in the bag before the game = 86 marbles
Number pf blue marbles were chosen = 24
Number of blue marbles = 40
Number of white marbles = 46 marbles
Total number of marbles = 40 + 46
= 86 marbles
Of the 40 blue marbles, 3/5 fraction were chosen
Number of blue marbles chosen = 40 × (3/5)
= 24 marbles
Part a
Number of bag's marbles were not chosen = 86 - 24
= 62 marbles
Part b
Number of marbles were in the bag before the game = 86 marbles
Part c
Number of blue marbles were chosen = 40 × (3/5)
= 24 marbles
Therefore, the 62 marbles were not chosen. There were 86 marbles before the game and number of blue marbles were chosen is 24 marbles
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write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8
A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
Define polynomial function.In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.
Given,
As stated, the polynomial's leading coefficient is equal to 1.
The function's zeroes are also listed as -2, 3, and 6.
For root 3: ( x - 3)
for root 6: (x - 6)
As a result, the polynomial function is
f = 1(x+2)(x-3)(x-6) (x-6)
f = (x+2)(x² - 6x - 3x + 18)
f = (x+2)(x² - 9x + 18)
f = x³ - 9x² + 18x + 2x² - 18x + 36
f = x³ - 7x² + 36
A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.
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11. Members of the student council are conducting a fundraiser by selling school calendars. After selling 80 calendars, they had a loss of $ 360. After selling 200 calendars, they had a profit of $600. Write an equation that describes the relation between y, the profit or loss, and x, the number of calendars sold. How much profit did they make from selling each calendar? How much would they have lost if they had sold no calendars?
a) The equation that describes the relation between x and y is y = 8x - 1000
b) They made 8% profit from selling the calendars
c) They will loss 1000 when they sold no calendars.
Given,
Members of student council had a loss of $360 after selling 80 calenders
They made a profit of $600 after selling 200 calenders.
y be the profit or loss
x be the calendars sold
We have to find the following;
a) The equation of the line in Slope-Intercept form is:
y = mx + b
Where "m" is the slope and "b" is the y-intercept.
We are aware that "y" here stands for the profit or loss and "x" for the quantity of calendars sold.
Then,
According to the exercise, the line passes through these two points:
(80, -360) and (200, 600)
Then,
We can find the slope of the line with the formula;
m = (y₂ - y₁) / (x₂ - x₁)
m = (-360 - 600) / (80 - 200)
m = -960/-120
m = 8
Now,
We can substitute the slope and one of those points into y = mx + b and solve for "b":
600 = 8 × 200 + b
-b = 1600 - 600
b = -1000
Then,
Substituting values, we get that the equation that describes the relation between the profit and loss and the number of calendars sold, is:
y = 8x - 1000
b) The slope of the line is the profit they made from selling each calendar
Profit = 8
c) The y-intercept is the amount they would have lost if they had sold no calendars:
b = -1000
They'd have lost $1000 if they had sold no calendars.
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use exponential fitting to find a closed formula for the sequence: 4, 5, 7, 11, 19, 35, 67, ...
The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.
The given sequence is - 4, 5, 7, 11, 19, 35, 67, ...
the first term - [tex]t_1[/tex] is 4
Hence, we can write the sequence as follows-
4 + [tex]2^0[/tex] = 5
5+[tex](2)^1[/tex]=7
7+[tex](2)^2[/tex]=11
11+[tex](2)^3[/tex]=19
and so on.
Here, we are adding the previous term with the exponential form of 2.
thus, we can conclude that -
[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]
where, x is a set of whole numbers, and n is a set of natural numbers.
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A surveyor needs to measure the distance, AB, across the lake. Beginning at E, he locates the midpoint, C, of AE and
the midpoint, D, of BE. He then measures CD. What is AB?
AB= m
4
49 m
Answer What is the midpoint of /AB? =b. point G
Step-by-step explanation:
AB is the abbreviation of “artium baccalaureus,” which is the Latin name for the Bachelor of Arts (BA) degree. It's a liberal arts degree, so it emphasizes the humanities, languages, and social sciences fields
g give a derivation to show that the following argument is valid in tfl. be sure to submit your answer by clicking the submit button.
g give a derivation to show that the following argument is valid in tfl. be p ∨ q) → r, p → s, ¬s → ¬r
1. (p ∨ q) → r Premise
2. p → s Premise
3. ¬s → ¬r Premise
4. p Assumption
5. s Modus Ponens (2, 4)
6. ¬r Modus Ponens (3, 5)
7. ¬(p ∨ q) Assumption
8. ¬p Simplification (7)
9. ¬q Simplification (7)
10. r Addition (1, 9)
11. Contradiction (6, 10)
12. ¬¬(p ∨ q) Double Negation (7-11)
13. (p ∨ q) Simplify(12)
14. r Modus Ponens (1, 13)
15. p → r Hypothetical Syllogism (4-14)
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Determine whether the graph represents a function. Explain.
Answer:
No.
Step-by-step explanation:
A function have only one output (y) for each x. This is not true with this graph. For example: the point (6,1) and ( 6,5) are both on the graph. The input 6 has more than 1 output. It has the output of 1 and 5. Since it has more than one output, it is not a function.
The steps your friend took to divide two mixed numbers are shown below.
4 2/3 / 2 1/4=14/3x9/4=21/2= 10½
Part A:
What should your friend change in order to divide the two mixed numbers correctly?
A) Find a common denominator of 3 and 4
B) Multiply by the reciprocal of 14/3
C) Multiply by the reciprocal of 9/4
D) Rename 4 2/3 as 3 5/3
Part B:
What should your friend do to check that their answer is correct using the inverse
operation?
The friend should change the multiplication of 9/4 to multiplication by the reciprocal of 9/4.
Option C is the correct answer.
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,
4(2/3) and 2(1/4)
Divide 4(2/3) by 2(1/4)
4(2/3) ÷ 2(1/4)
= 14/3 ÷ 9/4
Multiply the reciprocal of 9/4.
= 14/3 x 4/9
= 56/27
= 2(2/27)
Thus,
The value of the division of the fraction is 2(2/27).
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Which one of the following variables is a continuous variable?
a. The number of people on a bus.
b. The number of computers in a computer room in a school.
c. The height of Year 12 students in a high school.
d. The score out of 90 for a test.
Answer:
c.
Step-by-step explanation:
as this can take on any value (with as many digits after the decimal point as necessary) between certain interval limits.
all the others are usually either pure integers (and every real number in between them is not valid) or at most have finite fractions (like 1/2 or 1/4 points for scores, and between these no value is valid).
Two equalities that are equivalent
Answer:
there is 2/8 and 3/12 .they are both equivalent to each ,and equal 1/4.2 is 1/4 of because 2×4=8 is 1/4 of 12 because 3×4=12.
What percent of 75 is 36?
Answer:
48%
Step-by-step explanation:
Finding percents
P * 75 = 36
Divide each side by 75
P = 36/75
P =.48
Change to percent form
P = 48%
Answer:
48%%%%%
Step-by-step explanation:
The weight of meteorite A is 8times the weight of meteorite B. If the sum of their weights is 189 tons, find the weight of each.
The weight of meteorite A and B are 21 and 168 tons respectively.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, The weight of meteorite A is 8 times the weight of meteorite B. And the sum of their weights is 189 tons,
To find their weights we need to establish an equation, relating their weights,
Let weight of meteoroid B be x, then weight of meteoroid A will be 8x,
Establishing the equation,
8x+x = 189
9x = 189
x = 21
8x = 21x8 = 168
Hence, The weight of meteorite A and B are 21 and 168 tons respectively.
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the table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. which statements about the function described by the table are true? check all that apply. the independent variable is the number of people. the initial value (initial fee) for the picnic is $40. the rate of change is $8.67 per person. as the number of people increases, the total cost of the picnic increases. if 4 people attended the picnic, the total cost would be $46.
The correct statements are:
a) The independent variable is the number of people.
b) The initial value (initial fee) for the picnic is $40.
d) As the number of people increases, the total cost of the picnic increases.
A general linear equation is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:
m = (y - y')/x - x'
Now let's analyze the table:
The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:
(6, 52) and (9, 58).
Then the slope is:
a = (58 - 52)/9 -6 = 2
Then the line is something like:
y = 2*x + b
To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.
We will get:
52 = 2*6 + b
52 = 12 + b
52 - 12 = b = 40
Then the linear equation is:
y = 2*x + 40
Now let's see which statements are correct.
a) The independent variable is the number of people.
True, the "x" represents the number of people.
b) The initial value (initial fee) for the picnic is $40.
True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.
c)The rate of change is $8.67 per person.
False, the rate of change is equal to the slope, in this case is $2 per person.
d) As the number of people increases, the total cost of the picnic increases.
True.
e) If 4 people attended the picnic, the total cost would be $46.
To see if this is true or not, we just need to evaluate the function that we got in x = 4.
y = 2*4 + 40 = 48
So we can see that this is false.
Therefore, the correct statements are A, B, D
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Which of the following represents the series? (2 points)
–12 + (–5) + 2 + 9 + 16
sum from k equals 0 to 4 of negative 19 plus 7 times k
sum from k equals 1 to 5 of negative 19 minus 7 times k
sum from k equals 0 to 4 of negative 12 plus 7 times k
sum from k equals 1 to 5 of negative 12 minus 7 times k
The option that represents the arithmetic series is;
Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k
What is the formula for the arithmetic sequence?
An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.
The series is given as;
-12 + (-5) + 2 + 9 + 16
By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.
The series here is therefore an example of arithmetic sequence.
The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k
Where;
-12 is the first term
7 is the common difference
n is the number of terms
k = n - 1
When k = 0, we have;
-12 + 7·k
= -12 + 7 × 0
= -12
When k = 1, we have;
-12 + 7·k
= -12 + 7 × 1
= -5
When k = 2, we have;
-12 + 7·k
= -12 + 7 × 2
= 2
When k = 3, we have;
-12 + 7·k
= -12 + 7 × 3
= 9
When k = 4, we have;
-12 + 7·k
= -12 + 7 × 4
= 16
Therefore, we conclude that using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C
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The equation y = 2x + 3 is graphedbelow. If this graph is shifted up 3 units, what will be the equation of the new graph
Answer:
y = 2x + 6
Step-by-step explanation:
The equation is in point slope form or y = mc + b
where m is the slope and b is the y intercept
Since the graph is simply shifted up 3 units, the y intercept will change by increasing by 3, but the slope will not
This right circular cone has radius 2p and height
5p.
The dimensions are in centimetres.
The volume of the cone is 22500 cm³.
Work out the value of p
How do i work this out?
Answer:
p ≈ 10.24 cm
Step-by-step explanation:
r = 2p
h = 5p
Volume of a cone = (1/3)πr²h
22,500 = (1/3)π(2p)²(5p)
Now solve for p:
67500 = π4p²5p
67500 = π20p³
p³ = (67500)/π20 = 1074.3
p = ∛1074.3
p ≈ 10.24 cm
Part 1: Choose the equation represented by the model given below.
The linear equation that representing the given model is 6x-3 = 15.
In the given question, we have to choose the equation represented by the model given below.
As we know that;
A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.
The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.
To write the equation that represented by the given model, we count the variable that are of the same type. Then we write them after counting.
As we can see that in the model have 6 triangles of x, 3 circles of -1 and 15 circles of 1. So the linear equation that representing the given model is 6x-3 = 15.
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c) Assume that the sample points in each interval are right endpoints. Find the following sample points:x 1 = 0∘x 2 =08x 3=0 8
Each interval's sample points are at the right ends. sample points :x 1 = 0∘x 2 =08x 3=0 8 is 0°, 8°, 16°
Since the sample points in each interval are right endpoints, we need to find the points that are 8° apart.
The first sample point x1 is 0°. To find the next two sample points, we need to add 8° to the first sample point.
Therefore, the second sample point x2 = 8°, and the third sample point x3 = 16°.
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7 of 107 of 10 Questions
Question 1
Write the inverse variation equation for xand yif yvaries inversely with x,and y=34when x=8.
The inverse variation equation is
Question 2
Find ywhen x=12and find xwhen y=30.
If an answer is not an integer, enter it as a fraction.
When x=12, y=
Question 3
When y=30, x=
1. The equation of the inverse variation is, y = 272/x.
2. When x = 12, y = 68/3
When y = 30, x = 136/15.
What is an Inverse Variation?An inverse variation is defined by the equation, y = k/x, where k is the constant of proportionality between the relationship of y and x.
1. Given that y varies inversely with x, substitute y = 34 and x = 8 into y = k/x, and find the value of the constant of proportionality, k:
34 = k/8
34 × 8 = k
k = 272
To write the equation, substitute k = 272 into y = k/x:
y = 272/x
2. When x = 12, we have:
y = 272/12
Simplify
y = 68/3
When y = 30, we have:
30 = 272/x
30x = 272
30x/30 = 272/30
x = 136/15
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1) 2x+7x=
2) 8b-5b=
3) 5m+2m-4m=
4) a+a+a+a+a=
5) 2x+3x+6x-4x=
6) 2a+2b+a+3b=
7) 2x+7x-4=
8) 2m-2b-m+4b=
9) 10a+2b+2c+3a-b+4c=
10) 5+2 b-4+7 b=
11) 9 p+3 q-2 p-3 q=
12) a+2 b+a-b-10=
Answer: 1: 9x
Step-by-step explanation:
2: 3b
3: 3m
4: 5a
5: 7x
6: 3a+5b
7: 9x-4
8: m-6b
9: 13a+3b+6c
10: 1+9b
11: 7p
12: 2a+1b-10
rewrite 1/12 x^3 y + 5/12 xy^2 using a common factor
1/6 xy(2x2 + 5y)
1/6 x2y(2x + 5y)
1/12 xy(x2 + 5y)
1/12 x3y(y + 5)
The expression using the common factor is 1/12xy(x² + 5y)
How to rewrite the expression using the common factor?From the question, we have the following parameters that can be used in our computation:
1/12 x^3 y + 5/12 xy^2
Rewrite properly
So, we have
1/12x³y + 5/12xy²
Factor out 1/12 from the expression
So, we have the following representation
1/12(x³y + 5xy²)
Factor out x from the expression
So, we have the following representation
1/12x(x²y + 5y²)
Factor out y from the expression
So, we have the following representation
1/12xy(x² + 5y)
Hence, the expression is (c) 1/12xy(x² + 5y)
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Answer:The expression using the common factor is 1/12xy(x² + 5y)
Step-by-step explanation: