Answers
Answer: x=2, y=-8
Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution
to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case
so we have 13x-6y=22 and x=y+6
for the x value of the first equation, plug in x=y+6 from the second equation to get:
13(y+6)-6y=22
then you solve for y,
13y+78-6y=22
7y=-56
y=-8
then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6
so you'd have x=(-8)+6 to give you x=2
hope this helps!
Related Questions
Does anyone know the answer?
Answers
Answer:
Step-by-step explanation:
if you move over from 2. 3 full lines you get to 2.6. draw the x in between 2.6 and 2.8.
each line is 0.2 so 3.5 lines is 2.7
of 5 employees, 3 are to be assigned an office and 2 are to be assigned a cubicle. if 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?
Answers
The probability that the offices will be assigned to 2 of the men and 1 of the women will be 3/5
Lets find all the combinations of 2 men and 1 woman that can be chosen
(men, men, women) m m w
3/5 x 2/4 x2/3
(men, women, men) m w m
3/5 x 2/4 x 2/3
(women, men, men) w m m
2/5 x 3/4 x2/3
then just add those probabilities together:
= 3/5x2/4x2/3+3/5x2/4x2/3+2/5x3/4x2/3
= 12+12+12/60
this simplifies to 3/5
Simply put, probability measures how probable something is to occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics explains the examination of events that can occur subject to probability.
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I need help with problem 11.
Answers
Answer: 12-pound bag of cat food
Step-by-step explanation:
12 pounds bag of cat food = $18
15 pounds bag of cat food = $24
Let's find the cost per pound of the 12-pound bag first
Take 18 divided by 12 = $1.50 per pound
Now find the cost per pound of the 15-pound bag
Take 24 divided by 15 = $1.60 per pound
So, buying a 12-pound bag of cat food is better because it is cheaper per pound.
Charles spent 1/4 of his net salary on school fees,1/3 of the remainder on electricity and water bills.He then spent 1/9 of what was left on transport.If he finally had sh.3600,what was his net january salary
Answers
The net salary of Charles in the month of January is 8100.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, 'x' be the total salary of Charles in January.
Charles spent 1/4 of his net salary on school fees so the reaming amount is,
= {x - (1/4)x}
= (3/4)x.
(1/3)rd of the remainder on electricity and water bills which is,
= (1/3)×(3/4)x.
= (3/12)x.
= (1/4)x.
Now, The remaining amount is {(3/4)x - (1/4)x}.
= (2/4)x.
He then spent 1/9 of what was left on transport which is,
= (2/4)x×(1/9).
= (1/18)x.
Now, The remaining amount is {(2/4)x - (1/18)x}.
= [(18 - 2)/36]x.
= (16/36)x.
= (4/9)x.
So, as he left with 3600 it is equal to (4/9)x.
Therefore,
(4/9)x = 3600.
4x = 32400.
x = 8100.
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Adrian and his children went into a grocery store and will buy apples and
mangos. Each apple costs $2.25 and each mango costs $2. Adrian has a total
of $25 to spend on apples and mangos. Write an inequality that would
represent the possible values for the number of apples purchased, a, and the
number of mangos purchased, m.
Answers
We can represent the number of apples purchased by Adrian as the variable "a" and the number of mangos purchased by Adrian as the variable "m". The total cost of apples can be represented as $2.25 * a, and the total cost of mangos can be represented as $2 * m. The inequality that represents the possible values for the number of apples and mangos that Adrian can purchase is $2.25 * a + 2 * m <= 25.
8. Amy throws a ball so that when it is at its highest point, it passes through the centre of a
hoop. The path of the ball is modelled by the equation y=h+kx-x², where y is the
height in metres of the ball above the ground and x is the horizontal distance in metres
from the point at which the ball was thrown. The centre of the hoop is at the point where
x=2 and y = 5.
(a) Find the values of h and k.
(b) Find the value of x at which the ball hits the ground.
Answers
The values of h and k would be =2 and 2 respectively.
The value of x would be = 5.2
What is a horizontal distance?A horizontal distance is the distance that is be covered by a moving object through a horizontal pathway.
y = h + kx - 0.5x^2
When X = 2 and y = 5 is the centre of the hoop.
To calculate for y;
X max = -k/2× (-0.5)
X max = k = 2
y max = 5
Substitute the given variables into the equation and make h the subject of formula.
5 = (h + 2×2) - (0.5x^2)
5= (h + 4)- 1
h +4 = 5+1
h +4 = 6
h = 6-4
h = 2
Also from the graph, the value for x as the ball hits the ground would be = 5.2
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What do we mean by equidistant?
Answers
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.
For a triangle the circumcentre is a point equidistant from each of the three vertices. Every non-degenerate triangle has such a point. This result can be generalised to cyclic polygons: the circumcentre is equidistant from each of the vertices. Likewise, the incentre of a triangle or any other tangential polygon is equidistant from the points of tangency of the polygon's sides with the circle.
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Lauren builds a sandbox shaped like an octagon. Each side of the sandbox is the same length.
The perimeter of the sandbox is 18.8 feet.
An octagon with 8 equal sides, all with unknown length, in feet.
Part A
How long is each side of the sandbox? Enter your answer in the box.
feet ( Input Answer )
Part B
The total cost of sand to fill the sandbox is $59.48. Lauren and 3 friends divide the cost equally.
How much does each person pay? Enter your answer in the box.
$ ( Amount??? )
Answers
Answer:
To solve this problem, we need to first find the length of each side of the sandbox. Since the sandbox is an octagon with 8 equal sides, we know that the perimeter of the sandbox is 8 times the length of each side. Thus, we can use the formula for perimeter to find the length of each side:
Perimeter = 8 * Side Length
Substituting the given values into this formula, we get:
18.8 feet = 8 * Side Length
Dividing both sides of the equation by 8, we get:
Side Length = 2.35 feet
Therefore, each side of the sandbox has a length of 2.35 feet.
________________________________________________________
To find the amount of money that each person pays to fill the sandbox, we need to divide the total cost by the number of people involved. In this case, there are 4 people in total, so each person pays 1/4 of the total cost. Thus, the cost per person is $59.48 / 4 = $14.87.
Which of the following expressions are polynomials? Justify your answer:
(i) 8
(ii) sqrt 3x^2 −2x
(iii) 1− sqrt 5x
(iv) 1/5x −2 +5x+7
(v) (x−2)(x−4)/x
(vi) 1/x+1
(vii) 1/7 a^3 −1/sqrt 3a^2 +4a−7
(viii) 1/2x
Answers
(i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
What is polynomial?An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Name three types of polynomial.Monomial, binomial and trinomial are the three types of polynomials.
A polynomial may contain exponents, constants, and variables, but it never divides by a variable.
There cannot be a negative exponent in a polynomial.
No variable at all, one variable, two variables, or more are all possible for polynomials.
Exponents can only be multiples of 0, 1, or 2, not fractions.
Based on above definitions (i), (ii), (iv) and (vii) are the given expressions that represents polynomial.
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Please Help!! 25 points!!
Write the equation of the function in vertex form that has the vertex (1, 2) and the point (-3, 6). If necessary, use reduced fractions and not
decimals.
Answers
The equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
What is vertex form?
A different way to express the equation of a parabola is in its vertex form. A quadratic equation is typically represented as an x 2 + b x + c, and when graphed, it will look like a parabola.
Here, we have
Given
The vertex (1, 2) and the point (-3, 6).
we have to find the equation of the function in vertex form.
We know that
The vertex form of the equation is :
f(x) = a (x-h)² +k
Now, we put the value of x, h, and k and we get
6 = a(-3-1)² + 2
6 = 16a + 2
4 = 16a
a = 1/4
Now, we put the value of a in the vertex form equation and we get
f(x) = 1/4 (x-1)²+2.
Hence, the equation of the function in vertex form is f(x) = 1/4(x-1)²+2.
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I need help with this question.
Answers
Answer:
49
Step-by-step explanation:
Vertical angles are congruent.
8x-23=6x-5
8x-6x=23-5
2x=18
divide
x=9
8(9)-23
=49
A truck hauls a car cross-country. The truck's mass is 5.00x10 kg and the car's mass is 1.60x10 kg. If the force of propulsion resulting from the truck's turning wheels is 2.50x10' N, then determine the acceleration of the car (or the truck) and the force at which the truck pulls upon the car. Assume negligible air resistance forces. 3. Find the net forces for Situation 1 & 2 in page 56 of the module. 4. Figure below shows a truck is hauling a trailer along a level road. Find the force D that moves the truck forward. Use the given free body diagram. *27000 8500 0.7 m/? Drawbar D Trailer Truck
Answers
The truck is propelled forward by force D of 2.769 * 10⁴ N and acceleration of 0.78 m/s2.
What is Force?The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
Given, Mass of the truck = 5000 kg
Mass of car = 1600 kg
Force applied = 25000 N
As we know Force (F) =m.a
Where m = mass of the body
a = acceleration of the body
25000 = (5000 + 1600) * a
a = 25000/ 6600 = 3.7878.
a = 3.79 m/s²
According to diagram D = ma
m = 27000 + 8500 = 35500 kg
a = 0.78 m/s²
so D = 35500 * 0.78 = 27690N
Therefore, Force D that moves the truck forward is 2.769 * 10⁴ N, and acceleration is 0.78 m/s².
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What is rational function and irrational function?
Answers
The ratio of polynomials with which the polynomial denominator should not be equal to zero is known as a rational function. A function with a radical sign is frequently thought of as being irrational.
The ratio of polynomials to which the polynomial denominator should not be 0 is known as a rational function. It is same as the rational number's definition.
It's common knowledge that functions with radical signs are irrational functions. Activities including square roots, cube roots, or other roots, for instance, are regarded as irrational functions. It is claimed that a function is irrational if it performs addition, subtraction, multiplication, division, and raising to power with rational, non-integral exponents on the right side of the equation y = f(x).
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If (3x÷4,2)=(3,y÷6)then find the value of x and y.
Answers
Answer:
If you want to learn something without me directly giving you the answer, then here's the explanation
Step-by-step explanation:
You are given two points with unclear coordinates. Because they are equal to each other, you know that they are both the exact same point, meaning that the x and y coordinate of each point is equal to eachother. Therefore,
[tex]3x/4=3\\y/6=2[/tex]
If you understand basic algebra, the rest should be easy.
Is 1 is positive or negative?
Answers
The numeric value with no sign is positive so 1 is positive.
Can numeric value be negative?
There are whole numbers and fractional numbers, for instance, in the world of numerical data. There are both positive and negative numbers.
What is positive and negative in numbers?
Positive numbers are those that are greater than zero. It is possible to write positive numbers with or without a sign in front of them. A negative number is one that is less than zero. The minus symbol (-) is always written in front of negative values.
As 1 have no sign with it so it means 1 is positive. If any numeric value is negative it must have negative sign with it else numeric value is positive.
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Ben has a cellphone plan where he pays $12 per month plus $.10 per minute of talk time. The equation y=0.1x+12 can be used to find his monthly phone bill y given the number of minutes x he is talking. Which of the following, in set builder notation, represents a reasonable range of the function.
Answers
Answer:
A reasonable range for the function y=0.1x+12 would be all real numbers greater than or equal to 12. This is because the minimum monthly phone bill that Ben could have would be $12 (if he does not use any minutes), and the monthly bill can increase to any higher value depending on the number of minutes he talks. In set builder notation, this range would be written as {y | y >= 12}.
Step-by-step explanation:
(50/34.2)^1.5 = 10-t
Answers
(50/34.2)^1.5=10-t this equation is proved.
What is equation?An equation is a formula that is express the equality of two equation.
(50/34.2)^1.5=10-t
Covert decimal to integers
(500/342)^1.5 =10-t
Rearrange the variables to left side of the equation
t=10-(500/342)^1.5
Covert decimal to fraction
t=10(500/342)15/10
Simplify using a^n/m
Simplify using exponent rule with the same exponent(ab)^n=a^n.b^n
t=10-√250^3/171^3
Factor and rewrite the redicant in expotential form
T=10-√250^2×250/√171^2×171
Simplify the radical expression
t=10-1250√10×√19/513×19
Multiply number with radicals
t=1250√190/9747
Rewrite fraction using the latest common denominator
t=97470-1250√190/9747
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Select all that apply.
Which of the following are proportions?
2/8 = 3/12
3/4 = 8/10
25/10 = 5/2
3/4 = 15/20
Answers
Answer:
3/4 = 15/20
3/4 = 8/10
Step-by-step explanation:
Who invented [infinity]?
Answers
Infinity is a concept that refers to something that is unbounded, limitless, and endless. Mathematician John Wallis invented the standard sign for infinity,∞, in 1655.
Given that,
We have to find who invented the infinity.
We know that,
Infinity is a concept that refers to something that is unbounded, infinite, and endless. English mathematician John Wallis created the standard sign for infinity,∞, in 1655.
There are three basic categories of infinity: mathematical, physical, and metaphysical.
Examples of mathematical infinities are the quantity of points on a continuous line or the length of the never-ending series of the numbers 1, 2, 3, etc.
When one inquires if there are infinitely many stars or whether the universe will exist forever, they are posing spatial and temporal ideas of infinity.
There are issues about whether an ultimate entity must be infinite and whether lower things could also be infinite in a metaphysical discussion about God or the Absolute.
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Find the compositions for the given functions.
Answers
Answer:
x = 1
Step-by-step explanation:
f(x) = 5 - 6x g(x) = 3x -4
5 -6x = 3x - 4
5 = 9x - 4
9 = 9x
x = 1
There are 2 seats on the left side of a plane and three seats on the right. If there are 45 seats on the right, how many are on the left?
Answers
Answer:
30 seats
Step-by-step explanation:
For every row, there are 2 seats on the left and 3 seats on the right.
If there are 45 seats total on the right side, then there must be 45/3 = 15 rows. Therefore, there are 15*2= 30 seats on the left.
Julie wanted to match Lisa's obstacle course record of 74.6 seconds. She has already spent forty and one-fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
23.79 seconds
29.69 seconds
34.35 seconds
64.04 seconds
Answers
Julie has spent 40.25 + 10.56 = <<40.25+10.56=50.81>>50.81 seconds on wall climbing and the ropes.
She needs to complete the course in 74.6 - 50.81 = <<74.6-50.81=23.79>>23.79 seconds to match Lisa's record. Answer: \boxed{23.79}.
solve by substitution:
y = x
y=x+2
Answers
Answer:
Step-by-step explanation:
No solution.
y=x
-1(y=x)
-1y=-1x
+1y=1x+2
-1y and 1y cancel each other out. -1x and 1x cancel each other out.
Leaving +2..so it's a no solution. Solved using elimination it's easier..
How to make charts in Excel?
Answers
We can create charts in microsoft Excel by using new tab on the view menu.
What is microsoft Excel?It is a software programe created by Microsoft that uses spreadsheet to display numbers and data with formulas.It enables the users to format,organize and calculate data easily in a spreadsheet.
How to create charts in the Excel?Open Microsoft Excel and select new tab.
Enter the data you want to create a chart.
Click the insert tab.
Click the recommended charts.(chart type)
Create chart.(once you select the chart preview and description appear at the right).
Click OK.(The recommended chart inserted into worksheet).
Hence we can create Excel chart into worksheet or microsoft word.
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If I arrange my pawns in a square as large as possible, I have 7 left. If I had 6 more pawns, I could arrange all my pawns in a square without remainder would have one more pawn. How many pawns do I have?
Please give me an explanation!
Answers
Note that in the word problem above, the number of Pawns that you have is 14 pawns.
What is the rationale for the above answer?
To solve this problem, you can use the equation:
Number of pawns = (Number of pawns in the largest possible square) + (Number of pawns needed to fill in the square) + 1
Substituting the given information, we get:
Number of pawns = (7 pawns) + (6 pawns) + 1 pawn
Simplifying, we get:
Number of pawns = 14 pawns
Therefore, you have 14 pawns.
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Find the sum of -6x^2 + 3 and 4x^2 - 2x
Answers
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
What is polynomial?An algebraic statement with variables, coefficients, and mathematical operations like addition, subtraction, multiplication, or division is referred to as a polynomial. Let's talk about the definition of polynomials in this article, along with their types, uses, and standard form.Similar terms are added while adding polynomials, and similar terms are deleted when subtracting polynomials. Keep in mind that in mathematics, the sign following addition or subtraction will always be that of the variable with larger value.(4x^2 - 2x )+ ( -6x^2 + 3)
[tex]4x^2 - 2x + 0[/tex] +
[tex]-6x^2 + 0x + 3[/tex]
[tex]-2x^2 -2x +3[/tex]
Resultant polynomial is [tex]-2x^2 -2x +3[/tex].
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What is the size of image if m is equal to 1?
Answers
The size of image if magnification m is equal to 1 is calculated to be 2m.
Given
Height of object = 1 m
Height of image = h'
Magnification = m = 2
The formula to calculate magnification is
m = h'/h
2 = h'/1
h' = 2 m
Therefore , the height of the image formed will be 2m.
Magnification is a concept of physics which refers to the process of enlarging an object , the object itself does not become physically larger, but just appears larger as projected on a screen.
The magnification can take two forms, microscopic magnification and telescopic magnification. When we insert a small thing, it appears larger due to microscopic magnification.
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Find the x and y intercepts of f(x) = 2x² + 7x - 9.
A. (1, 0); (-9/2, 0) and (0, -9)
B. (-1,0); (9/2,0) and (0-9)
C. (0, 1); (0, -9/2) and (-9, 0)
D. (1, 0); (-4, 0) and (0, -9)
O A
OB
O C
OD
Answers
Answer:
B
Step-by-step explanation:
The [tex]x[/tex] intercepts are where [tex]f(x)=0[/tex].
[tex]2x^2+7x-9=0 \\ \\ (2x+9)(x-1)=0 \\ \\ x=-\frac{9}{2}, 1[/tex]
The [tex]y[/tex] intercept is where [tex]x=0[/tex].
[tex]f(0)=2(0)^2+7(0)-9=-9[/tex]
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=3. 5x+4 represents the cost y of bowling x games. Interpret the parameters of the function.
Answers
The function is in the form of linear equation in two variables where y is the cost and x are number of games played.
Linear equation in two variables is referred to a function that can be expressed in the form y = ax + b where a, b are constant values and x and y are variables. x is the independent variable and y is the dependent variable. Here we have the function y = 3.5x + 4 and the independent variable x is the number of games played and dependent variable y is the cost of the games that are played. Now in the equation the additional fee is represented by the constant value 3.5 and the fee for shoe is represented by the number 4 and is not dependent as the shoe rent fee is constant and not depends on number of games played.
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if repeated samples of yogurt sales were taken, according to the central limit theorem, the mean of those repeated samples would tend to be normally distributed if the sample size is large enough. because the sample population is , it is safe to apply the central limit theorem, even if the sample size for each sample is 15. a.) uniformly distributed b.) positively distributed c.) normally distributed d.) negatively distributed
Answers
The correct option is C. It is safe to apply the central limit theorem, even if the sample size for each sample is 15, if the sample population is normally distributed.
The central limit theorem states that, if you take repeated samples of a population and calculate the mean of each sample, the distribution of the means of those samples will tend to be normally distributed, provided that the sample size is large enough. This means that, even if the original population is not normally distributed, the distribution of the means of the samples will tend towards a normal distribution as the sample size increases.
However, if the original population is already normally distributed, then you can apply the central limit theorem with a smaller sample size and still expect the distribution of the means of the samples to be normally distributed. Therefore, in order for it to be safe to apply the central limit theorem with a sample size of 15, the sample population must be normally distributed.
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