Answer:
(6, 5 )
Step-by-step explanation:
3x + 2y = 28 → (1)
5x - 3y = 15 → (2)
multiplying (1) by 3 and (2) by 2 and adding the result will eliminate y
9x + 6y = 84 → (3)
10x - 6y = 30 → (4)
add (3) and (4) term by term to eliminate y
19x + 0 = 114
19x = 114 ( divide both sides by 19 )
x = 6
substitute x = 6 into either of the 2 equations and solve for y
substituting into (1)
3(6) + 2y = 28
18 + 2y = 28 ( subtract 18 from both sides )
2y = 10 ( divide both sides by 2 )
y = 5
solution is (6, 5 )
Ryan has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 7.5 points for each visit to the movie theater. He needs 160 points for a free movie ticket. Write and solve an equation which can be used to determine vv, the number of visits Ryan must make to earn a free movie ticket.
Answer:
85+7.5v=160
7.5v=160-85
7.5v=75
V=75/7.5
V=10
Ryan would need to take 10 visits to get a free ticket.
BUILD PERSEVERANCE Part A Simplify the expression. (8x + 6) + (5 − x) − 2 (3x+1)
The expression is x + 9.Generally speaking, an expression is at its simplest form when it is most usable.
What is its most basic form?Generally speaking, an expression is at its simplest form when it is most usable. as in this: 5x + x 3.To simplify an expression, create a similar expression devoid of any identical terms. Therefore, we shall rephrase the expression using the fewest number of terms possible.Determine the domain before you can simplify a rational expression.The collection of all possible inputs to a function, including all potential values for the variables, that enable the function to function.Explanation:
8x + 6+5 - x - 6x - 2
= x + 9.
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Find the measure of MN
Answer:
60 degrees
Step-by-step explanation:
The total measure of a circle is 360 degrees.
360-140-100 = 120
Angles MON and NOP are equivalent which makes MN and NP equivalent.
120/2 = 60 degrees = MN
Geometry: Applications of All Right Triangles
Look at the attachments below to answer this question.
Given:
A length of a side of an equilateral triangle = 32 cm
Formula Used:
If in an equilateral triangle with side length 'a' then,
Area of an equilateral triangle = [(√3)/4] × a2
Calculations:
Area of an equilateral triangle = [(√3)/4] × 322
⇒ (1024 × √3)/4
⇒ 256√3 cm2
What is the HCF of the polynomials x6 3x4 3x^2 1 and x^3 3x^2 3x 1?
The HCF of the polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1 is 1
When we divide the polynomials f(x) / g(x) then we get f(x) = g(x) × q(x) + r(x). Assuming the degree of g(x) > degree of r(x).
If the remainder r(x) is zero, then q(x) is the highest common factor of polynomials.
Here, we have been given two polynomials x^6 + 3x^4 + 3x^2 + 1 and x^3+3x^2 + 3x + 1
Let f(x) = x^6 + 3x^4 + 3x^2 + 1 and g(x) = x^3 + 3x^2 + 3x + 1
We can write these polynomials as:
f(x) = x^6 + 3x^4 + 3x^2 + 1
f(x) = (x² + 1)^3
The factors of polynomial f(x) = x^6 + 3x^4 + 3x^2 + 1: 1 and (x² + 1)^3
And g(x) = x^3 + 3x^2 + 3x + 1
g(x) = (x + 1)^3
And the factors of g(x) = x^3 + 3x^2 + 3x + 1 : (x + 1)^3 and 1
Therefore, the HCF of the polynomials f(x) and g(x) = 1
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How do you check if a function has an inverse function?
We can check if a function has an inverse function using horizontal Line Test.
What is Function?
A relation between a collection of inputs and outputs is known as a function. In plain English, a function is an association between inputs in which each input is connect
horizontal Line Test
Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F does have an inverse if there are no horizontal lines that cross the graph of f more than once.
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How is the graphed system of equations classified?
Drag and drop words into the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A Response area system has at least one solution. A Response area system has an infinite number of solutions.
A system that has no solution is classified as inconsistent.
A system that has one and only one solution is classified as independent
The system of equation graphed is consistent and independent.
How to interpret the graph of linear equations?The equations given by the graph are expressed as;
3x - 4y = 32
3x + 5y = 24
Now, if we subtract eq 1 from eq 2, we will get;
5y - (-4y) = 24 - 32
9y = -8
y = -8/9
Put 8/9 for y in eq 2 to get;
3x + 5(8/9) = 24
3x = 24 - 40/9
3x = 176/9
x = 176/27
Now, to classify solution to equations, we say that;
1) When there is no solution, it is inconsistent.
2) When there is one and only one solution, it is independent
Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.
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Bart and April are purchasing a house with a 15-year, 2/1 ARM for $315,000 at 5. 85% with a 2/8 cap structure. What will the difference in
payments be from year 2 to year 3?
$309. 69
$595. 18
$333. 68
$86. 56
The monthly payment for this difference would be $1,361.21. An Adjustable Rate Mortgage (ARM) is a type of mortgage in which the interest rate on the loan changes over time.
An Adjustable Rate Mortgage (ARM) payment is based on various factors such as the loan amount, interest rate, and the terms of the ARM. The interest rate is usually tied to a specific financial index, such as the U.S.
Here is the calculation format for the difference in payments between year 2 and year 3 for Bart and April's mortgage:
Total amount to be paid for the mortgage: $315,000
Rate of interest: 5.85% (Depreciating rate)
Time = 2 years:
a. Remaining amount to be paid after 2 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)²
= $315,000 × (1 - 0.0585)²
= $279,223.01
Time = 3 years:
a. Remaining amount to be paid after 3 years:
Principal × (1 - Rate/100)^time
= $315,000 × (1 - 5.85/100)³
= $315,000 × (1 - 0.0585)³
= $262,888.46
Difference in payments from year 2 to year 3:
= Remaining amount after 2 years - Remaining amount after 3 years
= $279,223.01 - $262,888.46
= $16,334.55
The monthly payment for this difference would be $1,361.21, which is calculated by dividing the difference in payments by 12:
$16334.546/12 = $1361.21
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I would like help with this, please. Someone give me an answer in the next day or two.
Answer:
one solution
Step-by-step explanation:
The two lines cross at exactly one point. That means there is one solution.
write an equation that expresses the following relationship p varies derectly with d and inversly with the square of u. In your equation use k as the proportionality
P= kd/u^2 is the equation which expresses the following relationship p varies derectly with d and inversly with the square of u.
What is Equation?Equation is a mathematical statement that expresses the equality of two expressions. An equation is written as an expression containing an equal sign, with each side of the equal sign representing a mathematical expression. The purpose of an equation is to show the relationship between two or more variables, such as a change in one variable resulting in a change in another. Equations are used to solve problems in mathematics, physics, economics, and many other fields.
The equation states that p is directly proportional to d, and inversely proportional to u squared. This means that as d increases, p increases, and as u increases, p decreases. The constant of proportionality, k, is a measure of the strength of the relationship between p, d, and u.
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For the rhombus below, find the measures
Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
what is rhombus ?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.
given
There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.
The alternative interior angles are similar, hence Angle 3 = 39.
Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.
angle 4=51.
Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
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HELPPPPPPP MEEEEE
If a trapezoid has an area of 135cm^2 and it’s height is 10cm and one base is 12 cm, find the other base length.
thxxx <333
The length of other base is 15 cm.
The area of a trapezoid can be found by using the formula:
Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.
Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.
Area = (b1+b2) * h / 2 = 135cm^2
We can solve for the other base length by isolating b1
b1 = 2*Area/h - b2
b1 = 2*135/10 - 12 = 27 - 12 = 15
So, the other base length is 15 cm.
Therefore, The length of other base is 15 cm.
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there are 32 students who studied maths and 28 geography and 26 social science if there are total 40 students in school if they all studies one subject atleast then find maximum number of students who studied all subjects
The maximum number of students who studied all subjects is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total students = 40
Number of students who studied maths = 32
Number of students who studied geography = 28
Number of students who studied social science = 26
The maximum number of students who studied all subjects.
= Highest number of students who studied one subject - Least number of students who studied a subject
= 32 - 26
= 6
Thus,
6 is the maximum number of students who studied all subjects.
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Solve the inequality. Graph the solution.
-1/3h > or equal to 8
(step by step equation)
We can solve the inequality to get:
h ≤ -3
And its graph can be seen below.
How to solve the inequality?Here we have the following inequality:
-(1/3)*h ≥ 8
To solve the inequality, we need to isolate h.
So we can multiply both sides by -3 (notice that this will change the sign of the inequality symbol)
So we will get:
-3*(-1/3)*h ≤ -3*h
h ≤ -3
Now to graph this, we need to draw a closed circle at -3, and draw an arrow that gose to the left.
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A rectangle has a perimeter represented by the expression 4x−8. Which expression also represents this perimeter? 4(x-8), 2(2x-8), 2(2x-4), 4(2x-4)
The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)
How to determine the perimeter expressionFrom the question, we have the following parameters that can be used in our computation:
Perimeter = 4x - 8
Factor out 2 from the expression
So, we have the following representation
Perimeter = 2 * 2x - 2 * 4
So, we have
Perimeter = 2(2x - 4)
Hence, the perimeter is 2(2x - 4)
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What is the inverse of the inverse of P → Q?
The inverse of ∼P→∼Q is P->Q.
Given ∼P→∼Q
Its inverse, ∼(∼P)→∼(∼Q), means that P→Q.
If the hypothesis is correct but the conclusion is untrue, a conditional statement is false. If the statement in the example above read, "If you achieve good marks then you will not get into a good college," it would be untrue. A conditional statement that has been modified or rearranged is referred to as a related conditional. An if-then statement, also known as a conditional statement, is a set of hypotheses followed by a conclusion. It is noted that p→q. Read this: if p, then q.
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On may 4th, an investor writes one s&p 100 jan 185 put at 6. His maximum potential gain on this position is:
An investor writes a s&p 100 Jan. 185 put at $6 on May 4. In this situation, his function maximum potential benefit is $600.
Define function.We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.
what is benefit?A benefit is a positive outcome or advantage that results from something. It can refer to the positive aspects or advantages of a product, service, or action, and can be tangible or intangible. Benefits can include increased efficiency, cost savings, improved safety, increased customer satisfaction, and many other positive outcomes.
Here,
As a put buyer, the most you may lose is the premium you previously paid to purchase the put option.
The option price must be reduced to equal the strike price less any already-paid premium in order to break even.
The strike price less the premium is your maximum gain as a put buyer. The most bullish option strategy is thought to be purchasing call options.
This tactic allows the buyer of the call option the choice, but not the responsibility, to purchase the stock at a certain price at a precise moment.
Whenever the price of the security increases using this approach, the buyer benefits. A long position is one in which a call or put option is purchased or held.
Investors have the option of purchasing from or selling to the other investor at a predetermined price.
On the other hand, a short position is when you sell a call or put option. Writers must purchase from people holding long positions or buying options.
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On May 4th an investor writes on s&p 100 Jan 185 put at $6. his function maximum potential gain in this position is $600.
Define function.We could create a function with a codomain of sets of numbers and X being the set of individuals once more. For instance, create the function c so that its output c(x) is the number of offspring of each person x for which the codomain Y is the set of whole numbers.
Your maximum loss as a put buyer is the premium already paid to buy the put option. To break even the option price must be lowered to cover the strike price minus the premium already paid. Your maximum profit as a put buyer is the strike price minus the premium. Buying call options are considered the most bullish options strategy.
This strategy gives the call option buyer the right but no obligation to buy the security at a specific price at a specific time. With this strategy, the buyer benefits when the price of the security rises. Buying or holding a call or put option is a long position. Investors have the right to buy or sell to the writing investor at a specified price. Conversely selling or selling a call or put option is a short position. Writers must buy or sell from long position holders or option buyers.
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answer quick its due in ten minutes
The number of grams of sugar that would be in a 200 ml glass of juice, given the carton, is 13. 2 grams of sugar
How to find the number of grams of sugar ?In a 250 ml glass of juice, we would see 16. 5 g of sugar. Given this information, we can find the amount of sugar in a 200 ml of juice by using direct proportion.
The amount of sugar in 200 ml of juice is :
= ( Amount of sugar in 250 ml x Quantity of juice ) / Quantity of base quantity of juice
= ( 16. 5 x 200 ) / 250
= 3, 300 / 250
= 13. 2 grams of sugar
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How the Earth rotates around the sun and moon?
The Earth orbits the Sun and rotates around its own axis. The Moon orbits the Earth and is held in place by the Earth’s gravity. This is why the length of a day is gradually increasing over time.
The Moon’s gravitational pull causes the tides, which is why the ocean’s water level rises and falls. The gravitational pull of the Moon also affects the Earth’s rotation by slowing it down slightly. This is why the length of a day is gradually increasing over time.
The Earth orbits the Sun and rotates around its own axis, while the Moon orbits the Earth and is held in place by the Earth’s gravity. The Moon’s gravitational pull causes the tides and affects the Earth’s rotation by slowing it down slightly, resulting in a gradual increase in the length of a day.
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I don't know help! image of the question is below
The value of x from the given triangle is 7√2 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
From the given triangle, one of the angle in right angle triangle is 45°, opposite side is 7 units and hypotenuse is x units.
We know that, sinθ =Opposite/Hypotenuse
sin45°=7/x
1/√2=7/x
x=7√2 units
Therefore, the value of x is 7√2 units.
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How does Earth's rotation cause day and night ?
Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.
The half of the planet facing the Sun experiences daylight, while the half facing away from the Sun experiences darkness. This cycle repeats itself every 24 hours, resulting in the day and night cycle that we experience.
Earth's rotation causes day and night by rotating on its axis, with half of the planet facing the Sun and the other half facing away from the Sun. This cycle of daylight and darkness lasts for creating the day and night cycle that we observe.Earth's rotation is what causes day and night. As Earth rotates on its axis, half of the planet is facing the Sun, while the other half is facing away from the Sun.
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A juice container advertises it now contains 20% more juice. Originally, it had 27.5 ounces, how
much juice does it now contain?
Answer:
33 ounces
Explanation:
20% of 27.5 ounces is 5.5 ounces.
To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces
the perimeter of the trapezoid is 18x +18 find the missing length of the lower base
PLEASE HURRY
Answer:
Step-by-step explanation:
8x+18=2x+x+4x-3
8x+18=7x-3
perimeter = x+21
Write the coordinates of the vertices after a rotation 90 degrees counterclockwise around the origin.
Answer: J' (8, -9); K' (8, -2); L' (3, -2); M' (3, -9)
Step-by-step explanation:
A rotation of 90 degrees counterclockwise is (x, y) -> (-y, x), so
J (-9, -8) -> J' (8, -9)
First, you take negative 8 (y) of J and make it positive 8 for the x of J'. Then, take -9 (y) of J and switch it to x of J'.
You repeat this process for the rest of the points. X switches to Y with the opposite sign and Y switches to X but stays the same.
K (-2, -8) -> K' (8, -2)
L (-2, -3) -> (3, -2)
M (-9, -3) -> (3, -9)
What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
The solution of the given system of equations is x = -7/3 and y = 7.
The given system of equations is given as,
3x + 2y = 7
y = 3x + 11
To solve this system of equations, we need to eliminate one of the variables. We can eliminate y by subtracting the second equation from the first.
3x + 2y = 7
y = 3x + 11
⇒ 3x + 2y - y = 7 - 11
⇒ 3x + 2y - 3x - 11 = -4
⇒ 2y - 11 = -4
⇒ 2y = -4 + 11
⇒ 2y = 7
Now, substitute the value of y in the first equation to find the value of x.
3x + 2(7) = 7
⇒ 3x + 14 = 7
⇒ 3x = 7 - 14
⇒ 3x = -7
⇒ x = -7/3
Therefore, the solution of the given system of equations is x = -7/3 and y = 7.
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What are logarithms used for?
Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:
What are functions?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What are exponential function?The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
They are used for:
Solving exponential equationsCompressing dataMeasuring the Richness of a signalComparing quantitiesSolving problems in physics and engineeringIn finance, it is used for financial modelings, such as the Black-Scholes model for pricing optionsIn computer science, it is used for information theory in the analysis of algorithms, complexity theory, and data compression.To learn more about exponential visit:
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What is the value of x in the equation 2.5 6x 4 )= 10 4 1.5 0.5 x?
The value of x in this problem is 2.
Our given algebraic equation is 2.5 ( 6x - 4 ) = 10 + 4 ( 1.5 + 0.5x) and in this, we have to find the final value of x.
Use the transposing method to isolate the variable x and then solve for it.
distribute brackets on both sides of the equation.
= 2.5*6x - 2.5*4 = 10 + 4*1.5 + 4*0.5x
= 15x - 10 = 10 + 6 + 2x
collect terms in x to the left side and numeric values to the right side.
= 15x - 2x = 10 + 6 + 10
= 13x = 26
= x = 26/13 = 2
Therefore the final value of x in this equation will be 2.
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Write an exponential function to describe the given sequence of numbers,
10, 60, 360, 2160, 12960,.
The exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
The given series 10, 60, 360, 2160, 12960, ... is a geometric progression.
a = 10
The common difference r = 60/10 = 6
As we know the general formula of the nth term of a geometric series is
aₙ = a × [tex]r^{n-1}[/tex]
Now, put the values of a = 10, r = 6 and n in the general formula,
aₙ = 10 × [tex]6^{n-1}[/tex]
Therefore, the required exponential function to describe the given sequence of numbers, 10, 60, 360, 2160, 12960, ... is aₙ = 10 × [tex]6^{n-1}[/tex].
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Can you pls help me with this
Answer:
y = x - 2
Step-by-step explanation:
Slope intercept form of an equation: y =mx +bHere m is the slope and b is the y-intercept.
Choose any two points on the line.
(2,0) ; (0,-2)
Now, find the slope.
[tex]\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]= \dfrac{-2 - 0}{0 - 2}\\\\=\dfrac{-2}{-2}\\\\= +1[/tex]
m = 1.
Now, y = 1x + b
The (2 , 0) passes through the line. Substitute x = 2 and y = 0 in the above equation and find the value of 'b'.
0 = 1*2 + b
0 = 2 + b
-2 = b
Equation of line:
y = x - 2
If 16 inches of ribbon costs $2.08, how much will 36 inches of
ribbon cost? Show your thinking.
4.68
find unit rate by dividing 208 cents by 16 which is 13 than multiply by 36
Answer:
16 inches of ribbon cost- $2.08
36 inches of ribbon cost- ?
36*$2.08/ 16
$74.88/16
= $4.68
Thus, 36 inches of ribbon would cost $4.68