An equation of a line that is parallel to this line is y = -x + 3.
An equation of a line that is perpendicular to this line is y = x + 3.
An equation of a line that is neither parallel nor perpendicular to this line is y = 3x + 3.
How to write the required equations?Based on the information provided about this line, an equation that models it is given by:
4x + 4y = 4.
4y = -4x + 4
y = -x + 1
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -1 = -1
Slope (m) = -1
Therefore, the required equation is y = -x + 3
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-1 × m₂ = -1
m₂ = 1
Slope, m₂ = 1
Therefore, the required equation is y = x + 3
By using a line with a different slope other than 1 and -1 would produce a line that is neither parallel nor perpendicular to the given line.
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A student starts a walk at (−6, 10). If the student walks 4 miles north, south, east, or west, which of the following could be their location at the end of the walk?
HELP ME PLEASE!!!
Answer: Assuming the student walks along a rectangular grid and not diagonally, the possible locations the student could end up after walking 4 miles in any direction would be the points that are 4 units away from the starting point in a north, south, east, or west direction.
Using this information, we can determine that the possible locations the student could end up at are:
(-2, 10)
(-6, 14)
(-10, 10)
(-6, 6)
Therefore, the answer is:
All of the above locations are possible endpoints.
Step-by-step explanation:
If the student walks 4 miles north, south, east, or west, the location at the end of the walk are respectively, (-6, 14). (-6, 6), (-2,10). (-10, 10).
What is a coordinate plane?The Cartesian plane, named after the mathematician René Descartes (1596 - 1650), is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.
Given that,
A student starts a walk at (-6, 10)
If the student walks 4 miles north, south, east, or west,
The location at the end of the walk =
Plotting dotted diagram,
East
|
North --------- |-------------- South
|
West
Suppose, he goes to north direction
Then, 4 will be added to y coordinate,
It can be written as,
(-6, 14)
Similarly, for South, (-6, 6),
East, (-2,10).
West, (-10, -10)
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A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
Answer:
There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).
Step-by-step explanation:
A quadrilateral has opposite sides with the same slopes and consecutive sides with slopes that are reciprocals. What is the most precise classification of the quadrilateral?
Quadrilateral
Rectangle
Parallelogram
Trapezoid
The most precise classification of the quadrilateral with opposite sides having the same slopes and consecutive sides having slopes that are reciprocals is a Rectangle.
1. Opposite sides with the same slopes imply that these sides are parallel.
2. Consecutive sides with slopes that are reciprocals mean that they are perpendicular.
3. Parallel opposite sides make the quadrilateral a parallelogram.
4. Perpendicular consecutive sides make it a rectangle, as all angles are 90 degrees.
So, the quadrilateral is a Rectangle.
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does the line ever match up perfectly? can the lines ever have the same slope? can the lines ever have the same y-intercept? why or why not?
No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.
No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.
If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.
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help
I need this asap
Answer: natural number=11
integer= -4
irrational= pi, 0.1010010001.....,root 5
rational= 0.1212...., -3/5,0.3,2 1/4
Step-by-step explanation:
There are 36 students in the school choir. The ratio of girls to boys in the choir is
5:4. Two girls are absent from practice on Monday. What is the ratio of girls to
boys at choir practice on Monday?
A 3:4
C 9:8
B 5:2
D 10:7
Answer:
C 9:8
Step-by-step explanation:
total students = 36
5+4=9
5:4 = 20:16
20-2=18
ratio for monday = 18:16
=9:8
Consider parallelogram ABCD below. Point E is the intersection of diagonals AC and BD.
Progress: 0/2
Part 1 of 2
4(-2,2)
D(-2,-10)
(a) Find the area of AABE.
cm
2
B (8.2)
C(8.-10)
tanner is 2 years older than kiara. in 8 years the sum of their ages will be 80. how old is tanner now?
Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
Tanner is currently 16 years old. Kiara is 14 years old. We can use algebra to solve this problem.
Let x be Tanner's age and y be Kiara's age. We can write the equation x + y = 80.
Since Tanner is two years older than Kiara, we can write x = y + 2. Substituting x for y + 2, we can write (y + 2) + y = 80.
Simplifying this equation, we get 2y + 2 = 80. We can subtract 2 from both sides of the equation, leaving us with 2y = 78. Dividing both sides by 2 gives us y = 39.
Since y represents Kiara's age, we know that Kiara is currently 39 years old. Since Tanner is two years older, we can say that Tanner is 41 years old.
Therefore, Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
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19. INVESTMENTS Kent invested $5000 in a retirement plan. He allocated x dollars of the money to a bond account
that earns 4% interest per year and the rest to a traditional account that earns 5% interest per year.
a. Write an expression that represents the amount of money invested in the traditional account.
b. Write a polynomial model in simplest form for the total amount of money T Kent has invested after one year.
(Hint: Each account has A + IA dollars, where A is the original amount in the account and I is its interest rate:)
c. If Kent put $500 in the bond account, how much money does he have in his retirement plan after one year?
Part a: Expression for conventional account: $(5000-x) at 5%pa.
Part b: polynomial model: T = 5250 - 0.01x
Part c: Sum of investments in retirement account: T= $5245.
Explain about the bond account?When they need to raise money, governments and businesses issue bonds.
a. Create an expression to show how much money is invested in the conventional account.
Back $(5000-x) at 5%pa
b. Construct a polynomial model in its simplest form to represent the entire sum of investments made by T. Kent after a year (possibility: thus every account has A + iA dollars, in Which a is the account's initial balance and I is the interest rate).
The bond will increase to after a year to : x + 0.04x
= x(1+0.04)
= 1.04x ...eq 1
So, after the time of one year this traditional account growth will be-
(5000-x) + 0.05(5000-x)
= 5000 - x + 0.05*5000 - 0.05x
= 5000 - x + 250 - 0.05x
= 5250 - 1.05x ..eq 2
From eq 1 and eq 2
T = 1.04x + 5250 - 1.05x
T = 5250 - 0.01x
c. If Kent invested $500 in bonds, how much will he have in the retirement account in a year?
x=500
T= 5250 - 0.01*500
T= 5250 - 5
T= $5245
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help pls its too much
Answer:
24.13
Step-by-step explanation:
when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
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DUCK is a rectangle. Solve:
X=
UDK=
For the rectangle, the value x will be 14 and angle UDK will be 35°.
What exactly is a rectangle?
A rectangle is a four-sided polygon with four right angles (90-degree angles). It has opposite sides that are equal in length and parallel to each other. The rectangle is a special case of a parallelogram, where the opposite sides are also parallel. The two sides that are equal in length are called the "width" or "short side", while the other two sides are called the "length" or "long side". The area of a rectangle is found by multiplying its length by its width, while its perimeter is found by adding the lengths of all four sides.
Now,
As we know all angles of a triangle are 90°.
then 5x-15+2x+7=90
7x=98
x=14
and in triangle UDK
sum of all angles = 180°
∠UDK+90+5x-15=180
∠UDK=180-145
∠UDK=35°
Hence,
the value x will be 14 and angle UDK will be 35°.
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a coffee distributor needs to mix a(n) kenya coffee blend that normally sells for $8.20 per pound with a breakfast coffee blend that normally sells for $14.00 per pound to create 10 pounds of a coffee that can sell for $9.36 per pound. how many pounds of each kind of coffee should they mix?
The coffee distributor should mix 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend to make 10 pounds of a coffee blend that can sell for $9.36 per pound.
We can use the idea of weighted averages to overcome this issue. Assume that 10 pounds of the desired blend require x pounds of Kenya coffee blend and y pounds of morning coffee blend.
The price of the Kenya coffee mix per pound is $8.20, while the price of the morning coffee blend per pound is $14.00. The required combination costs $9.36 per pound. On the basis of the weighted average, we can construct the following equation:
8.20x + 14.00y = 9.36(10) (10)
When we simplify this equation, we obtain:
8.20x + 14.00y = 93.60
Given that we are producing 10 pounds of the ideal blend, we also know that x + y = 10. To get the values of x and y, we can use substitution or elimination to solve this system of equations.
Use substitute now. We can find x from the second equation by solving in terms of y:
x = 10 - y
Substitute this into first equation, we get:
8.20(10 - y) + 14.00y = 93.60
82 - 8.20y + 14.00y = 93.60
5.80y = 11.60
y = 2
We obtain x = 8 by substituting y = 2 into x = 10 - y. Hence, to manufacture 10 pounds of a coffee mix that can be sold for $9.36 per pound, we'll need 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend.
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Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
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Polygon WXYZ is dilated by a scale factor of 3 with vertex W as the center of dilation, resulting in polygon W’X’Y’Z’. The coordinates of point ware (3,2), and the coordinates of point X are (7,5).
So the coordinates of point X' after dilation are (15, 11).
Polygon WXYZ is dilated by a scale factor of 3, with vertex W as the center of dilation. This means that the distances from vertex W to the other vertices are multiplied by 3, while W remains unchanged. Given the coordinates of point W are (3,2) and point X are (7,5), we can find the coordinates of point X' after dilation.
To do this, first determine the change in the x and y coordinates from point W to point X:
Δx =[tex]7 - 3 = 4\\[/tex]
Δy =[tex] 5 - 2 = 3[/tex]
Now multiply these changes by the scale factor of 3:
Δx' =[tex] 4 * 3 = 12[/tex]
Δy' =[tex] 3 * 3 = 9[/tex]
Now add these new changes to the original coordinates of point W to get the coordinates of point X':
X'(x) =[tex] W(x) + Δx' = 3 + 12 = 15[/tex]
X'(y) = [tex]W(y) + Δy' = 2 + 9 = 11[/tex]
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165. 1% of 384. 7. Round to the nearest thousandth
Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.
In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:
Step 1: We make the assumption that 384.7 is 100% since it is our output value.
Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.
Step 3: In the same sense, x% = 165.1.
Step 5: Now, we have a pair of simple equations:
100% = 384.7 --(1).
x% = 165.1 ---(2).
Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.
Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7
=> x = ( 165.1/384.7) × 100
=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.
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Select ALL the set of numbers that are possible values for x in the inequality, x<-3
The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)
To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.
{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.
{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.
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Complete Question:
Select all the sets of numbers that are possible values for x in the inequality, x<-3.
{5,7,9}{-9, -7, -5}{-33, -22, -11}{-5,0,5}Evaluate. Write your answer as a fraction or whole number without exponents.
6^–3 =
Answer:
i'm pretty sure it's 33
Step-by-step explanation:
6^= 36
36-3= 33
according to census 2000, asians in the united states represent about what percent of the total population? question 1 options: 16.2 percent 10.5 percent 3.6 percent
Answer: 4.2 percent
Step-by-step explanation: Your welcome
Write an equation to describe the relationship between t, the number of tickets, and c
, the total cost of tickets
The relationship between t, the number of tickets, and c, the total cost of tickets is: c = 55t
Relation between two variables, i.e, total cost and number of tickets:
The statistical relationship between two variables is called their correlation. The correlation can be positive, which means that the two variables move in the same direction, or negative, which means that when the value of one variable increases, the value of the other variable decreases.
Based n the Question:
Since there is no processing fee and the ticket price remains the same, we know that the fee will be proportional to the number of tickets purchased. The general form of the equation expressing the proportional relationship between the cost (c) and the number of tickets (t) is:
c = kt
where k is the constant of proportionality (the cost per ticket).
We can find k by using any of the data points given in the table. Using the first point, we have :
110 = k·2
Dividing the equation by 2:
110/2 = k = 55
Then using this value for k, the desired equation can be written:
c = 55t
Complete Question:
Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),
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Find explicit formulas for sequences of the form a1, a2, a3, ... with the initial terms given
0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7
This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
Notice that the sequence alternates between positive and negative terms and that the denominators of each term increase by 1 while the numerators increase by 1 or -1. To find the explicit formula, we can write it in terms of its general form:
a1 = 0
a2 = -1/2
a3 = 2/3
a4 = -3/4
a5 = 4/5
a6 = -5/6
a7 = 6/7
We can see that the numerator of each term is equal to its index number, n, if n is even and equal to -n if n is odd. The denominator of each term is equal to n+1 for all terms.
Using this observation, we can write the explicit formula for the sequence as:
an = (-1)^(n+1) * n / (n+1)
where (-1)^(n+1) is equal to -1 if n is odd and 1 if n is even. This formula generates the sequence 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7, ...
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The price of a 6-minute phone call is 1. 80. What is the price of a 18-minute phone call?
Answer:
5.40
Step-by-step explanation:
let X represent the price of a 18 minute phone call
X=18 ×1.80
6
= 5.40
Find the equation of L
[tex]y=\frac{7}{2.4} x-6[/tex] ; if estimated then : [tex]y=\frac{7}{2.5} x-6[/tex]
Explination:
Y-intercept is -6, (0,-6)
The rise over run it [tex]\frac{7}{2.4} x[/tex]. The denominator is 2.4 because it nearly 2.5.
PLEASE HELP
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
Answer: 64πa^2-192πa+144
Step-by-step explanation:
Area of a circle: π •r^2
So then the area would be: 4•π(4a-6)^2
FOIL (4a-6)(4a-6) and get 16a^2-48a+36
Plug it in and get 4•π(16a^2-48a+36)
Distribute pi sign and get 4•(16πa^2-48πa+36π)
Distribute the 4 and you get 64πa^2-192πa+144
Answer: 64πa^2-192πa+144
please help quick
6d = 54
answer
6 divided by 54 is equal to 9
therefore
answer = d=9
the temperature at 12 noon was 10 degree Celsius above zero .if it decreases at the rate of 2 degree Celsius per hour until midnight ,at what time would the temperature be 8 degree Celsius below zero? what would be the temperature at midnight?
Answer:
The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.
siona bought 10 outfits to wear to church. the shirt has a price of $3.50 and a pair of shorts has a price of $4.00. how many shirts and pairs of shorts did she buy when she spent a total of $36.50?
Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.
Let's use a system of equations to solve this problem:
Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:
Equation 1: x + y = 10 (Siona bought 10 outfits in total)
Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)
To solve for x and y, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can solve for x in terms of y:
x = 10 - y
Substitute this expression for x into Equation 2:
3.50(10 - y) + 4.00y = 36.50
Simplify and solve for y:
35 - 3.50y + 4.00y = 36.50
0.50y = 1.50
y = 3
Now we can substitute y = 3 back into Equation 1 to solve for x:
x + 3 = 10
x = 7
Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.
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Which of the filling best describes the expression 6(y+3)
Answer: 6y+18
Step-by-step explanation:
6 x y=6y
6 x 3= 18
Answer:
The product of a constant factor of six and a factor with the sum of two terms.
Step-by-step explanation:
Since we have given that
6(y+3)
It has sum of two terms i.e. y and 3.
Mathematically, it is expressed as
y+3
And the product of constant factor of six and a factor with the sum of two terms.
Mathematically, it is expressed as
6(y+3)
Hence, The product of a constant factor of six and a factor with the sum of two terms.
How is the distributive property used when finding the product of two polynomials?
Write a phrase in words for each algebraic
expression.
22. m+83_
23.42s
24. 9/d
25. t - 29
26. 2+g
27. 11x
28. h/12
29. 5- k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
what is expression ?An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.
given
The sum of m and 83.
Forty-two times s.
Nine divided by d.
t decreased by 29.
Two more than g.
Eleven times x.
h divided by twelve.
Five minus k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
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