The estimated solution of the system 3x + y = 10 and y = 6x + 1 is (1, 7)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the linear equation:
3x + y = 10
y = -3x + 10 (1)
y = 6x + 1 (2)
Subtracting equation 2 from 1 to solve using elimination method gives:
0 = -9x + 9
9x = 9
x = 1
put x = 1 in eqn 2:
y = 6(1) + 1
y = 7
The solution is (1, 7)
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Uri buys two burgers and a soda for $\$2.10$, and Gen buys a burger and two sodas for $\$2.40$. How many cents does a soda cost
The cost of soda as calculated from the data given is found to be as 0.9 cents.
the price of 1 burger = x
the price of 1 soda =y
Therefore, the equation for Uri and Gen becomes,
2x + y = $2.10
x+ 2y = $2.40
On solving these two equations we will get the value of x and y which represents their cost.
on multiplying equation 2 with 2 , we will get ,
2x + 4y = 4.80
Therefore , on subtracting equation 1 and 2 ,
2x + y = $2.10
- 2x + 4y = 4.80
=> -3y = - 2.7
=> y = 0.9
Therefore x will be ,
x+ 2y = $2.40
x+ 2(0.9) = $2.40
x + 1.8 = $2.40
x = 2.40 - 1.8
= 0.60
Therefore, cost of soda is 0.9 cents.
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A cat can run 30 miles per hour. At this rate, how many minutes would it take a car to run 1.5 miles?
Answer:
3 minutes
Step-by-step explanation:
30÷1.5=20
1h=60mins
60÷20=3minutes
In 6-7, explain whether each graph represents a linear function.
Answer:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.
Step-by-step explanation:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.
Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.
which of the following inequalities orders the numbers 0.1, 0.04, and 1/6 from least to greatest?
Answer:
0.04 < 0.1 < 1/6
Step-by-step explanation:
Solve the differential equation by variation of parameters. y + 2y' + y = e^-t ln t y(t)=
The general integral is provided by y = C1e-t + C2te-t + (1/2)(t2)e-t.
(m + 1)2 =0 is the characteristic polynomial for the differential equation y" +2y' + y = e-t.
Roots -1, -1. yh = C1e-t + C2te-t is the answer to the homogeneous equation at that point.
Use the method of variation of parameters, taking into account the independent integrals y1 = e-t, y2 = te-t, and Wronskian
W(t) = e-2t, to derive the specific integral related to f(t) = e-t.
Then, use the conventional formula yp = - y1(t)(Integral of Y2(t)f(t)dt/W(t)) +y
Obtain yp = (1/2)(t2)e-t for the given situation.
As a result, the general integral is provided by
y = C1e-t + C2te-t + (1/2)(t2)e-t.
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becky is doing research in which she needs 28 g of a substance that is 30% protein how many grams of each two ingredients one that is 50% protein in the other 25% protein should she mix together
Answer:
25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.
Step-by-step explanation:
To make 28 grams of a substance that is 30% protein, Becky will need to mix together different ingredients to get the desired amount of protein.
Let's call the amount of the first ingredient (50% protein) "x" and the amount of the second ingredient (25% protein) "y".
We know that:
The total amount of the mixture is 28 grams
The mixture is 30% protein
The first ingredient is 50% protein
The second ingredient is 25% protein
We can set up the following equations to represent the problem:
x + y = 28 (the total amount of the mixture is 28 grams)
(0.50)x + (0.25)y = 0.30(28) (the mixture is 30% protein)
Now we can use the first equation to solve for one variable in terms of the other. If we solve for y, we get:
y = 28 - x
We can substitute this into the second equation:
(0.50)x + (0.25)(28-x) = 0.30(28)
Which gives us:
0.50x + 7 - 0.25x = 8.4
And further simplifying
0.25x = 0.6
x = 2.4
Now we know that the first ingredient, which is 50% protein, makes up 2.4 grams of the mixture. We can use this information to find the amount of the second ingredient:
y = 28 - x = 28 - 2.4 = 25.6 grams
So, Becky needs to use 2.4 grams of the first ingredient (50% protein) and 25.6 grams of the second ingredient (25% protein) to make 28 grams of the mixture that is 30% protein.
Unit rates are ALL AROUND US. If you have a phone, take a picture of a unit rate that you find at the grocery store, gas station, or as you are simply out and about. For your post, describe the picture and where you found your unit rate and what the unit rate was.
For your replies, think back and see if you recall seeing unit rates in those places. Describe how a unit rate could be used at the location where it was found.
A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.
What is a unit rate?In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.
What is an example of a unit rate that you can find at a grocery store?A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.
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A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $18. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Let S be the amount of money the salesperson needs to sell in a week to earn the same amount with the two options. The salesperson earns 40 * $18 = $<<40*18=720>>720 with Option A.
We can set up the following equation to represent the amount of money the salesperson earns with Option B:
0.04S = $720
Solving for S, we find that the salesperson needs to sell $720 / 0.04 = $<<720/0.04=18000>>18,000 to earn the same amount with Option B.
12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill ______ holes in 25 minutes.
Step-by-step explanation:
12 holes / 6 minutes = 2 holes / 1 minute
the simplified ratio is 2/1 = 2.
so, for 25 minutes we need to keep the same ratio :
x holes / 25 minutes = x/25 = 2
x = 2×25 = 50
it drills 50 holes in 25 minutes.
108% of 75.5 is what number
Answer:
81.54
Step-by-step explanation:
% of a # = (% * #)/100
% = 108
# = 75.5
(108 * 75.5)/100
8,154/100
81.54
OR
% of a # = (%/100) * #
% = 108
# = 75.5
(108/100) * 75.5 = 1.08 * 75.5
81.54
The row-echelon form of the augmented matrix of a system of equations is given. Find the solution of the system.
The solution of the system of equations is:
x = 5t - 4
y = -5t + 1
z = t
Option B is the correct answer.
What is a matrix?A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.
We have,
From the row-echelon form of the augmented matrix of a system of equations, we get,
x + 0y -5z = -4
x - 5z = -4
x = 5z - 4
0x + y + 5z = 1
y + 5z = 1
y = -5z + 1
0x + 0y + 0z = 0
Now,
Put z = t (any real number)
We get,
x = 5t - 4
y = -5t + 1
Thus,
The solutions are:
x = 5t - 4
y = -5t + 1
z = t
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Coach Taylor asked his team to record the distance they ran during practice. It’s a dot plot so someone plssss help me I’ll give them 10 points!
The range between 3/16 & 3/8 is where the line plot with the difference of daily mileage logged by each racer in a group is still most obvious.
Line plot: what is it?A line graph, liner plot, or line chart is a graph that uses lines to link the individual data points. For a specific time period, quantitative values are displayed as a line graph. Line graphs are widely used in finance to depict the past market movements of a securities or asset.
Here,
calculation
The number line indicates that there's more than or equal to 3 marks when there are 7 markings either on or to the right of 3. The fraction must first have the same denominators.
=> 3/8 x 2 = 6/16
=> 1/2 x 8 = 8/16, 3/8 x 2 = 6/16
=> 5/8 x 2 = 10/16, 1/2 x 8 = 8/16
Since they all have the same numerator, we can now compare them.
=> 3/16 - 1/16 = 2/16
=> 6/16 - 3/16 = 3/16
=> 8/16 - 6/16 - 2/16
=> 10/16 - 8/16 = 2/16
The largest distinction is between 3/16 and 3/8 (6/16 vs. 3/16).
The range between 3/16 and 3/8 is where the line plot with the difference in daily mileage logged by each runner in a group is most obvious.
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The complete question is " Coach Taylor asked his team to record the distance they ran during practice The line plot shows the number of miles the individual members in a group of runners run each day. How many runners run at least 3 miles per day?."
Neville buys a triangular box with three chocolate cauldrons. The box is an equilateral triangle with three circles with a radius of 6 inches inscribed inside it. What is the perimeter of the triangle?
Using the radius of the circle given, the perimeter of the equilateral triangle is 48 inches
What is Perimeter of Equilateral TriangleThe perimeter of an equilateral triangle is three times the length of one side. Thus, if the length of one side is 'l', the perimeter of the triangle is 3l.
In this problem, the equilateral triangle has 3 circles inside with radius of 6 inches each.
Assuming the circles when combined will cover the entire triangle.
The diameter of the circle = 6 * 2 = 12 in
The length of the equilateral triangle = 2 * 12 = 24in
However, we already know the perimeter of an equilateral triangle is three times the side length of the triangle.
Perimeter of equilateral triangle = 3 * 24
Perimeter = 48 in
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Mrs. Remeto separate would like to buy a television TV set payable for 6 months starting at the end of the month how much is the cost at the TV set if her monthly payment is P3,000 and interest is 9% compounded semi annually?
If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.
The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.
According to our question-
9% = 0.09 / 2
=0.045 + 1 =1.045^(1/6)
=1.00736312 - 1 x 12 x 100
=8.836%
PV=0;
PMT=3000;
R=0.08836/12; N=6; PV
=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)
PV==17,545.08
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How do you find the f of G in a pair of functions?
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
f of G in a pair of functions ,
Let a example that f(x) = [tex]x^{2}[/tex] and g(x) = √x + 2
To find f(g(x)), we take f(x) and everywhere there's an x, we replace it with g(x).
f(x) = x2
f(g(x)) = g(x)2
= (√x + 2)2
= x + 2√x + 4
To find the domain of f(g(x)), find the domain of both the inner function g(x) and the resultant function f(g(x)) and then compute the intersection.
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How to do elimination with 3 variables?
Elimination is a method used to solve systems of linear equations with two or more variables. One possible method to solve a equation with 3 variables using elimination is solving algebraically.
To use elimination to solve a system of equations with three variables, you can follow these steps:
1. Write the system of equations. For example, if you have the equations:
3x + 2y - z = 5
2x - 4y + 2z = 6
5x - 2y + 3z = 10
2. Multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say y in two of the equations.
3. Next, you can multiply one of the equations by a scalar (a number) so that one of the variables has opposite coefficients, say x in two of the equations.
4. Now substitute this value of z in the first or the second equation to solve for x
5. Now substitute this value of x and z in the second equation or any other equation to solve for y
This is one possible way to use elimination to solve a system of equations with three variables. Depending on the specific problem, there may be different ways to eliminate variables, but the general idea is to use scalar multiplication and addition or subtraction to create a new equation with one variable having the same coefficient but with opposite signs. One can also use Gaussian elimination or matrix inversion method.
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The circle below has center H. Suppose that mLFEG=46°. Find the following.
From given circle, Measure of arc FG = 23πr/45 and ∠FHG = 92°.
The distance between the two locations along a segment of a curve is known as the arc length. Any portion of the circumference is an arc in a circle. The angle that an arc occupies at any given point is the angle created by the two line segments that connect that point to the arc's endpoints.
Length of an Arc = r, where is in radians, is the formula used to express the arc length of this arc OP.
The measure of ∠FHG = 2 × 46° [As Angle at center equals twice at circumference]
So, ∠FHG = 92°
Measure of the arc FG = 2πr(θ/360°)
FG = 2πr(92/360)
FG = 23πr/45
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What are polynomials and its different types explain with examples?
Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
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).
A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.
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a) 3.2 ÷ 0.8 = ? please explain how you got it and b) 7.5 ÷ 0.5 also please explain how you got it i'll give the brain thing
Answer: To solve a division problem of the form a ÷ b = c, you need to find the value of c that makes the equation true. This means that if you multiply b by c, the result should be equal to a.
a) In the problem 3.2 ÷ 0.8 = ?, we are looking for the value of c that makes the equation true.
To solve this problem, we can multiply 0.8 by c to find the value of c that makes the equation true:
0.8 * c = 3.2
Dividing both sides of the equation by 0.8, we get:
c = 4
Therefore, the value of c that makes the equation 3.2 ÷ 0.8 = ? true is 4.
b) In the problem 7.5 ÷ 0.5 = ?, we are looking for the value of c that makes the equation true.
To solve this problem, we can multiply 0.5 by c to find the value of c that makes the equation true:
0.5 * c = 7.5
Dividing both sides of the equation by 0.5, we get:
c = 15
Therefore, the value of c that makes the equation 7.5 ÷ 0.5 = ? true is 15.
P.S. I don't need a brainliest, i am just happy that I am helping someone
Step-by-step explanation:
Solve for x: -24 = 6x
Answer:
x = -4
Step-by-step explanation:
Solve for x: -24 = 6x
-24 = 6x
x = -24 : 6
x = -4
---------------------
check
-24 = 6(-4)
-24 = -24
the answer is goodWhen Edna's phone is fully charged, it can operate for up to 18 hours before running out of battery. It has been 6 hours since Edna's phone was fully charged. Let x represent how many more hours Edna's phone can operate without running out of battery. Which inequality describes the problem? 6 + x < 18 6 +xs 18 Solve the inequality. Then, complete the sentence to describe the solution. Edna's phone can operate for up to more hours without running out of battery.
Edna's phone can operate for up to 12 more hours without running out of battery.
In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
fully charged
T = 18Hr
It has been 6 hours since Edna's phone was fully charged.
remaining battery =18- 6= 12Hr
x=12Hr
6 + x < 18
6 +x > 18
neither nor.
both equations are wrong.
6 +x = 18
Edna's phone can operate for up to 12 more hours without running out of battery.
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Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation.
Hint: Use the change of base formula: log base b of y equals log y over log b.
''By taking log'' on both side Mike solve this equation.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 37ˣ = 12
Now,
Since, The expression is,
⇒ 37ˣ = 12
Solve this expression as;
⇒ 37ˣ = 12
Taking log both side, we get;
⇒ log 37ˣ = log 12
⇒ x log 37 = log 12
⇒ x = log 12 / log 37
⇒ x = 1.08 / 1.57
⇒ x = 0.69
Thus, The value of x = 0.69
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The following system of equations is _____.
y = - x +
2x + 6y = 4
independent
inconsistent
equivalent
Answer:
"equivalent"
Step-by-step explanation:
Right!!
Select all the true equations.
Group of answer choices
5+0=0
LaTeX: 15\cdot0=015 ⋅ 0 = 0
1. 4 + 2. 7 = 4. 1
LaTeX: \frac{2}{3}\cdot\frac{5}{9}=\frac{7}{12}2 3 ⋅ 5 9 = 7 12
LaTeX: 4\frac{2}{3}=5-\frac{1}{3}
The true equations are - 15·0 = 015·0, 1.4 + 2.7 = 4.1, and 4(2/3) = 5-(1/3).
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is -
5 + 0 = 0
This equation is false, as if 0 is added to any number, the result is the same number itself, and not 0.
The second equation is -
15·0 = 015·0
Any number multiplied by 0, gives the result as 0.
In the above equation LHS = RHS = 0.
Hence, this equation is true.
The third equation is -
1.4 + 2.7 = 4.1
Solving LHS -
= 1.4 + 2.7
= 4.1
So, LHS = RHS and hence, this equation is true.
The fourth equation is -
(2/3) · (5/9) = 7/12
Solving LHS -
= (2/3) × (5/9)
= 10/27
Here, LHS ≠ RHS.
Hence, this equation is false.
The fifth equation is -
4(2/3) = 5-(1/3)
Solving LHS -
4(2/3) = 14/3
Solving RHS -
= 5 - 1/3
= (15 - 1)/3
= 14/3
Therefore, LHS = RHS and hence, this equation is true.
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Finding zeros of this equation
Answer:
01?
Step-by-step explanation:
I didn't see a picture so maybe just one
What is the solution to this system of linear equations 2x 3y equals 3?
The solution to this system of linear equations is x = 3, y = 2.
2x - 3y = 3
2x = 3 + 3y
2x = 3y + 3
x = (3y + 3) / 2
x = 3/2 + 3/2y
x = 3, y = 2
This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.
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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.
1. Rewrite the equation in standard form is
2x + 3y = 3
2. Subtract 2x from both sides of the equation:
3y = 3 - 2x
3. Divide both sides by 3:
y = (3 - 2x)/3
4. Solve for x by substituting y in the original equation:
2x + 3(3 - 2x)/3 = 3
5. Simplify and solve for x:
2x + 3 - 2x = 3
x = 1
6. Substitute x into the equation y = (3 - 2x)/3
y = (3 - 2(1))/3
y = -1/3
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Which equation describes a line with a slope of 2/5 that passes through (0,4)
Answer: y = 2/5x + 4
Step-by-step explanation:
We will write a point-slope form equation for this line, then simplify it into a slope-intercept form equation.
Given point-slope form:
➜ m is the slope
➜ (x1, y1) is the point given
y - y1 = m(x - x1)
Substitute values in:
y - (4) = (2/5)(x - (0))
Distribute 2/5:
y - 4 = 2/5x - 0
Add 4 to both sides of the equation:
y = 2/5x + 4
Step-by-step explanation:
since we have the slope and a point, we can start with the point-slope form
y - y1 = a(x - x1)
a is the slope, (x1, y1) is the given point.
y - 4 = (2/5)(x - 0) = 2x/5
y = 2x/5 + 4
or
y = (2/5)x + 4
How do you solve for 4=2+W over 2
Need to know immediately
Solving for W in the equation 4 = (2 + W) / 2 gives W = 6
How to solve for WUsing the equation 4 = (2 + W) / 2, W is solved by making it the subject of the formula and this is means placing W alone at the left hand side of the equation'
This is achieved by the following procedure
clearing the fraction
4 = (2 + W) / 2,
8 = 2 + W
rearranging the equation
W + 2 = 8
subtracting 2 from both sides of the equation
W + 2 - 2 = 8 - 2
since 2 - 2 = 0 we have
W = 6
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Are isosceles triangles always 180?
No, isosceles triangles are not always 180 degrees. The sum of the interior angles of an isosceles triangle is 180 degrees, but the individual angles can be different.
Isosceles triangles do not necessarily have a 180-degree angle. Any triangle with two equal sides is said to be isosceles. Any triangle's internal angles add up to 180 degrees. An isosceles triangle's individual angles can change depending on how long its sides are, though. An isosceles triangle, for instance, might have a third side that is longer or shorter than the other two sides if the first two sides are equal. The size of the inner angles will be impacted by this. As a result, an isosceles triangle need not have angles that are 180 degrees. An isosceles triangle has interior angles that add up to 180 degrees, but the individual angles might vary.
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A plane slices a double-napped cone parallel to the slanted edge of the cone. Which conic section is formed?
Circle
Ellipse
Hyperbola
Parabola
It is both of the pair of intersecting lines and degenerate hyperbola.
What is conic section?A conic section, conic or quadratic curve is a curve formed by the surface of a cone crossing a plane. The hyperbola, parabola, and ellipse are the three forms of conic sections; the circle is a special case of the ellipse, however it was frequently referred to as a fourth type. Parabolas, ellipses, circles, and hyperbolas are the four main forms of conics. Examine the diagrams below to discover how a conic is defined geometrically. The plane does not travel through the vertex of a non-degenerate conic.
Here,
It consists of a pair of intersecting lines as well as a degenerate hyperbola.
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