A function is an equation that has a single solution for each value of y.
How to prove that two functions are equal?When two functions f and g share a domain and a codomain, and f(a)=g is true for each an in the domain, we say that the two functions are equal (a).
A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).
If two functions share the same domain and codomain as well as the same values across the board, then they are considered to be equal.
In spite of how the elements are arranged in the sets, two sets are said to be equal when all of their components are present in both. Afterward, the sets are referred to as equal sets. When all of one set's elements are absent from the other, two sets are said to be unequal.
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Help me please i dont not know the answer
Answer:
i believe the answer would be both c and f
Segment KM is parallel Segment JN. What is the scale factor?
Answer:first option
Step-by-step explanation:
La diferencia de dos numeros mas otro numero en lenguaje algebraico
Podemos escribir "La diferencia de dos numeros mas otro numero" como:
(x - y) + z
¿Como escribir usando lenguaje algebraico?Queremos escribir "La diferencia de dos numeros mas otro numero"
Pimero, recordar que la diferencia entre dos numeros se refiere a la resta entre dos numeros, entonces podemos empezar escribiendo:
(x - y)
Donde x e y son los dos numeros de los que tomamos la diferencia.
Y a esto le debemos sumar otro numero, que puede ser otra variable z, entonces obtendremos:
(x - y) + z
Esta es la expresion usando lenguaje algebraico.
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15 Answer:
A local gym charges nonmembers $10 per hour to use the tennis courts.
Members pay a yearly fee of $300 and $4 per hour for using the tennis
courts. Write an equation to find how many hours, h, you must
use the tennis courts to justify becoming a member.
16 Answer:
Solve the equation in question #15 for the value of h.
Answer:23.45
Step-by-step explanation:
Selecting the number two out of the following
list of numbers: 1, 3, 2, 5, 7, 4, 9, 2, 8
Height Consider the fountain shown. The initial velocity of the stream of the water is 48 feet per second. The velocity v of the water at any time t (in seconds) is given by v = 48 − 32t. Find the time for a drop of water to travel from the base to the maximum height of the fountain. (Hint: The maximum height is reached when v = 0.)
A drop of water will reach the maximum height after 1.5s.
How long takes a drop of water to reach the maximum height?The velocity of the water is modeled by the linear equation:
v(t) = 48 - 32t
And the water reaches the maximum height when the velocity is zero.
Then we just need to solve the equation below:
48 - 32t = 0
48 = 32t
48/32 = t
1.5 = t
So it takes 1.5 seconds for a drop of water to reach its maximum height.
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100 POINTS PLEASE HELP THERE IS A PIC JUST PLEASE CLICK ON IT PLEASEEEE
Answer:
[tex]2.48\times 10^{-2}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{\left(1.24 \times 10^2\right)\left(3.6 \times 10^{-3}\right)}{1.8 \times 10}[/tex]
Remove the parentheses in the numerator:
[tex]\implies \dfrac{1.24 \times 10^2 \times 3.6 \times 10^{-3}}{1.8 \times 10}[/tex]
Collect like terms in the numerator:
[tex]\implies \dfrac{1.24 \times 3.6 \times 10^2 \times 10^{-3}}{1.8 \times 10}[/tex]
Multiply the numbers 1.24 and 3.6:
[tex]\implies \dfrac{4.464 \times 10^2 \times 10^{-3}}{1.8 \times 10}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{4.464 \times 10^{2-3}}{1.8 \times 10}[/tex]
[tex]\implies \dfrac{4.464 \times 10^{-1}}{1.8 \times 10}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a \times b}{c \times d}=\dfrac{a}{c} \times \dfrac{b}{d}:[/tex]
[tex]\implies \dfrac{4.464}{1.8} \times \dfrac{10^{-1}}{10}[/tex]
Divide the numbers 4.464 and 1.8:
[tex]\implies 2.48\times \dfrac{10^{-1}}{10}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 2.48\times 10^{-1-1}[/tex]
[tex]\implies 2.48\times 10^{-2}[/tex]
10. A doctor's office schedules 10-minute and 20-minute appointments. The doctor also makes hospital rounds
for four hours each weekday. Suppose the doctor limits these activities to, at most, 30 hours per week. Write
a lincar inequality to show the number of 10-minute and 20-minute appointments the doctor can schedule and
graph the solutions. What are three possible solutions to the problem?
Three possible solution of this problem are(x = 10, y = 0)(x = 6, y = 3),(x = 0, y = 6).
What is inequality?Inequality is the unequal distribution of resources, opportunities, and advantages among different people. It can be caused by a variety of factors, such as discrimination, unequal access to education, lack of economic opportunities, or social exclusion. Inequality has a negative effect on society, as it can lead to poverty, health issues, and a lack of economic growth. It is important to address inequality in order to create a more equitable society and ensure everyone has the same opportunities for success.
Linear Inequality: 10x + 20y ≤ 30,(x = 6, y = 3),
where x is the number of 10-minute appointments and y is the number of 20-minute appointments.
Graph:
The graph of the linear inequality 10x + 20y ≤ 30 is a half-plane, with a boundary line of 10x + 20y = 30 and a solution region of 10x + 20y ≤ 30.
Possible Solutions:
1) 10 10-minute appointments and 0 20-minute appointments (x = 10, y = 0)
2) 6 10-minute appointments and 3 20-minute appointments (x = 6, y = 3)
3) 0 10-minute appointments and 6 20-minute appointments (x = 0, y = 6).
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A company is reviewing a batch of
products to determine if any are defective. On average,
of products are defective.
95.99% probability that the company will find 2 or fewer defective products in this batch and 0.66% probability that 4 or more defective products are found in this batch.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The binomial probability is the probability of exactly x successes on n repeated trials.
[tex]P(X=x)=C_{n,x} .p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} =\frac{n!}{x!(n-x)!}[/tex]
And p is the probability of a success on a single trial.
24 products means that n=24
3.2% are defective, thus p=0.032
The probability that 2 or fewer are defective is:
P(X≤2)=P(X=0)+P(X=1)+P(X=2)
In which P(X=0)=0.4582
P(X=1)=0.3635
P(X=2)=0.1382
0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.
The probability that 4 or more are defective is:
P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)
=0.4582+0.3635+0.1382+0.0335
P(X≥4)=1-P(X<4)
=1-0.9934
=0.0066
0.0066 = 0.66% probability that 4 or more defective products are found in this batch.
Hence, 95.99% probability that the company will find 2 or fewer defective products in this batch and 0.66% probability that 4 or more defective products are found in this batch.
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-8x + 2 > 0Solve the following inequalities. Be sure to follow the rules for operations with signed numbers.
[tex]-8x+2 > 0[/tex]
Subtract 2 from both sides:
[tex]-8x+2-2 > 0-2[/tex]
[tex]-8x > -2[/tex]
Divide both sides by -8:
[tex]\dfrac{-8x}{-8} > \dfrac{-2}{-8}[/tex]
(Since we are dividing by a negative number, the sign will reverse)
[tex]x < \dfrac{1}{4} \texttt{ or }x < 0.25[/tex]
L1 is parallel to L2, and therefore m∠t=m∠x and m∠w=m∠y. Which can be used to show that the sum of the interior angles of the triangle is 180°? Responses A straight angle has a measure of 180°, so m∠t+m∠v+m∠w=180°, and since m∠t=m∠x and m∠w=m∠y, m∠x+m∠y+m∠v=180°. A straight angle has a measure of , so m∠t+m∠v+m∠w=180°, and since m∠t=m∠x, , and m∠w=m∠y, m∠x+m∠y+m∠v=180°. Alternate interior angles are equal, so m∠t=m∠x and m∠w=m∠y, and since ∠x and ∠y are supplementary, m∠x+m∠y+m∠v=180°.Alternate interior angles are equal, so m∠t=m∠x, , and m∠w=m∠y, and since ∠x and ∠y, , are supplementary, m∠x+m∠y+m∠v=180°. Since m∠t=m∠x and m∠w=m∠y, and m∠v=90°, the sum of the angles is m∠x+m∠y+m∠v=180°.Since m∠t=m∠x and m∠w=m∠y, and m∠v=90°, the sum of the angles is m∠x+m∠y+m∠v=180°. The interior angles of a triangle are complementary, so since m∠t=m∠x and m∠w=m∠y, m∠x+m∠y+m∠v=180°. The interior angles of a triangle are complementary, so since m∠t=m∠x, , and m∠w=m∠y, m∠x+m∠y+m∠v=180°.
Mike has jelly beans worth $5 per pound that he wants to mix with 10 pounds of jelly beans worth $2 per pound to get a mixture that he can sell for $4.25 per pound. How many pounds of the expensive jelly beans should he use?
By solving an algebraic equation we will see that Mike needs to use 30 pounds of the $5 jelly beans.
How many pounds of the expensive jelly beans should he use?Mike wants to mix beans worth $5 per pound with 10 pounds of jelly beans worth $2 per pound to get a mixture that he can sell for $4.25 per pound
If he uses x pounds of the $5 beans, then we can write the equation:
x*$5 + 10*$2 = (10 + x)*$4.25
And now we can solve that equation for x.
$5*x + $20 = $42.50 + $4.25*x
$5*x - $4.25*x = $42.50 - $20
$0.75*x = $22.50
x = $22.50/$0.75
x = 30
So Mike needs to use 30 pounds of the $5 beans.
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Solve equation 3x+2x+4=39
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
[tex]3x+2x+4=39 \\ \\ 5x+4=39 \\ \\ 5x=35 \\ \\ x=7[/tex]
Use the unit circle to find the value of sin (-90)
The value of Sin(90) is equal to 1.
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: Sin(90) and to find the value using the unit circle
Rotate ‘r’ anticlockwise to form a 90° angle with the positive x-axis.
The sin of 90 degrees equals the y-coordinate(1) of the point of intersection (0, 1) of unit circle and r.
The value of sin 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of sin 90° is equal to the y-coordinate (1). ∴ sin 90° = 1.
Hence, Sin (90) is equal to 1.
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The measure of one angle of a right triangle is 56∘ more than the measure of the smallest angle. Find the measure of the smallest angle.
Subtract 90 from 180, which is 90 degrees.
Then you get the equation of 2x+56 = 90 for which the 2 represents the split between the 90 degrees and the +56 is the 56 degrees higher than the smaller angle.
Solving this gives you x = 17 degrees, which is the small angle.
For 17+56 = 73 = larger angle
17+73 = 90 plus the other 90 gives you 180 total.
Answer:
The smallest angle is 17°
Step-by-step explanation:
All the angles add up to 180°. Use this to write an equation.
x = smallest angle
x+56 = not the smallest angle
90 = the right angle
x + x+56 +90 =180
combine like terms
2x + 146 = 180
subtract 146
2x = 34
divide by 2
x = 17
The smallest angle is 17°.
see image.
(Look at picture) and ty btw <3
The system of inequalities to represent this real-world scenario is
[tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]
Explain the system of inequalities?A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are utilised.Polynomial inequality, rational inequality, and absolute value inequality are the many forms of inequalities that can exist in mathematics.A system of inequalities can be solved by graphing each individual inequality and then determining where the multiple solutions overlap.Multiply all terms by the fractions' least common denominator to get rid of any fractions.Simplify the inequality by merging like words on either side.To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts.Given data :
Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
[tex]\left \{ {{x + y \leq 450} \atop {7x + 4y \leq 1150}} \right.[/tex]
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May someone help me on questions 3, and 6
please?
For the given question the two triangles are similar the length of side WX = XY.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
The two triangles XWZ and XZY are similar triangles based on ASA criteria.
Since, the two triangles are similar the length of side are also equal.
Hence, WX = XY.
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Please help ill give brainliest
The diagram showing parallel lines and the related angles is used to fill the information
d Nail salon
c Community Center
g Library
e Gas Station
a Clothing Store
f Pet Store
h Restaurant
b Park
What is same side exterior angle?Two angles that are inside (between) the two lines, more especially on the same side of the transversal, are referred to as same side inside angles.
Vertical angels are the angles that are the opposite angles formed when two lines cross. They are equal to each other.
Angles with the same size that are found on opposing sides of the transversal line are known as alternate angles. Angles that alternate are equal:
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Is the relation shown below a function? Use the graph and justify your answer. (0, 0), (2, 0), (2, 2), (3, 4) and (6, 6) A coordinate plane with 4 points plotted: one is at the origin, one is 2 units to the left of the origin on the x axis, one is 2 units above the last point, and one is 4 units above and 3 units to the right of the origin. Yes, each x-value has a unique y-value. Yes, each y-value has a unique x-value. No, two points have different y-values for the same x-value of 2. No, two points have different x-values for the same y-value of 2.
The relation (0, 0), (2, 0), (2, 2), (3, 4) and (6, 6) is not function.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
(0, 0), (2, 0), (2, 2), (3, 4) and (6, 6).
Now, we now that any relation is said to be function if the every input value have their corresponding value and the input value should be distinct.
So, there is no two input values repeat.
Then, the given relation is not a function because in the relation the same input value 2 have output 0 and 2.
Hence, the relation is not function.
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Attendance is decreasing at a rate of 0.5% per year. If there are 1200 people attending now how many will be attending in 4 years?
Answer: There will be approximately 1154.6 people attending.
Step-by-step explanation:
To find out how many people will be attending in 4 years, we can use the formula:
Attendance(future) = Attendance(current) * (1 - rate)^time
Where:
Attendance(current) = 1200 people
Rate = 0.5% (as a decimal = 0.005)
Time = 4 years
So, Attendance(future) = 1200 * (1 - 0.005)^4
Attendance(future) = 1200 * 0.99^4 = 1200 * 0.9605 = 1154.6 people
So, in 4 years, there will be approximately 1154.6 people attending.
Evaluate the following expressions. Your answer must be an exact angle in radians and in the interval
the solutions of the following expressions are:
a) π/6
b) - π/6
c) - π/4
What is trigonometry?Trigonometry is the field of mathematics that deals with certain angles' functions and how to use such functions in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.
The lengths, heights, and angles of various triangles are studied in relation to one another in mathematics. The field was created around the third century BC as a result of the use of geometry in astronomical research.
a)
tan ⁻¹ (√3/3)
= tan ⁻¹ (1/√3)
= tan ⁻¹ (tan π/6)
= π/6
b)
tan ⁻¹ (-√3/3)
= tan ⁻¹ (-1/√3)
= tan ⁻¹ (tan - π/6)
= - π/6
c)
tan ⁻¹ (-1)
= tan ⁻¹ (tan - π/4)
= - π/4
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You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
You:
Friend:
Your tutor for ___ hours.
1)
You tutor for 9 hours.
2)
You tutor for 4 hours.
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,
From the tap diagram,
1)
You have three parts.
A friend has one part.
This means,
4 parts = 12 hours
1 part = 3 hours
Now,
You = 3 parts = 3 x 3 = 9 hours.
2)
You have two parts.
A friend has four parts.
This means,
6 parts = 12 hours
1 part = 2 hours
Now,
You = 2 parts = 2 x 2 = 4 hours.
Thus,
You tutor for 9 hours.
You tutor for 4 hours.
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1+6x+1+ 8= 1+ 7x + 2x
Answer:
x = 3
Step-by-step explanation:
Solve for x:
6 x + 1 + 1 + 8 = 7 x + 2 x + 1
Grouping like terms, 6 x + 1 + 1 + 8 = 6 x + (1 + 1 + 8):
(6 x + (1 + 1 + 8)) = 7 x + 2 x + 1
1 + 1 + 8 = 10:
6 x + 10 = 7 x + 2 x + 1
Grouping like terms, 7 x + 2 x + 1 = (7 x + 2 x) + 1:
6 x + 10 = ((7 x + 2 x) + 1)
7 x + 2 x = 9 x:
6 x + 10 = 9 x + 1
Subtract 9 x from both sides:
(6 x - 9 x) + 10 = (9 x - 9 x) + 1
6 x - 9 x = -3 x:
-3 x + 10 = (9 x - 9 x) + 1
9 x - 9 x = 0:
-3 x + 10 = 1
Subtract 10 from both sides:
(10 - 10) - 3 x = 1 - 10
10 - 10 = 0:
-3 x = 1 - 10
1 - 10 = -9:
-3 x = -9
Divide both sides of -3 x = -9 by -3:
(-3 x)/(-3) = (-9)/(-3)
(-3)/(-3) = 1:
x = (-9)/(-3)
The gcd of -9 and -3 is -3, so (-9)/(-3) = (-3×3)/(-3×1) = (-3)/(-3)×3 = 3:
Answer: x = 3
Answer:
X = 1
Step-by-step explanation:
start by simplifying both sides
6x + 10 = 1 + 9x
Next, subtract 6x from both sides
10 = 1 + 9x
Next subtract 1 from both sides
9 = 9x
Divide by 9 from both sides
X = 1
Which of the following functions is graphed below?
A. y=|x-4|-2
B. y= |x-4|+2
C. y =|x+4|-2
D. y =|x+4|+2
Answer: C, y=|x+4|-2
Step-by-step explanation:
I have access to a Desmos Calculator.
Find the volume of a square based pyramid with a base length of 10 and a height of 14.
Volume of a square pyramid with base length (a) 10 and height(h) 14 is
466.67 cubic units.
What is a pyramid ?A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex. It has a polygonal basis and is a conic solid. There are n + 1 vertices, n + 1 faces, and 2n edges in a pyramid with an n-sided base. Every pyramid is dual in itself.
A pyramid with a square base is known as a square pyramid. It is a right square pyramid with symmetry if the apex is perpendicular to and above the square's center. It is an equilateral square pyramid, the Johnson solid, if all edge lengths are equal.
A square pyramid has the following characteristics:
5 Faces.Triangles make up the 4 side faces.It has a square base.It has 8 Edges and 5 Vertices (corner points).Volume of a square pyramid with base length (a) 10 and height(h) 14 is
V = (1/3)*(a)²h = 10²*14/3 = 466.67 cubic units.
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Given that the focus of a parabola is (−3, −5/4) and the directrix is y=−3/4, what is the equation of the parabola? Please help me
Answer: The equation of a parabola is given by (y + 1/4) = 2*sqrt(10)x where the vertex is (0, -1/4) and the distance between the vertex and the focus is 2sqrt(10)
This equation is derived by using the standard form equation of a parabola and the given focus and directrix values.
Step-by-step explanation: A parabola can be defined by the set of points that are equidistant to the focus (F) and the directrix (d). The standard form equation of a parabola is (y - k) = 4p(x - h) where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix. In the given scenario, the focus is (-3, -5/4) and the directrix is y = -3/4. By using these values we can find the distance between the vertex and the focus which is 2sqrt(10) and the vertex is (0, -1/4). Then we can substitute these values into the standard form equation to get the equation of the parabola (y + 1/4) = 2sqrt(10)*x.
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Q2: Determine whether the graphs of each pair of equations are parall
perpendicular or neither.
1. y = 3x + 4
y = 3x + 7
3. y = 2x-5
y = 5x -5
5. y = 3/5x - 3
5y = 3x - 10
7. y = 7x + 2
x + 7y=8
2. y = -4x+1
4y = x + 3
4. y=-1/3x + 2
y = 3x - 5
6. y = 4
4y = 6
8. y = 5/6x - 6
x + 5y = 4
Answer:
The graphs of y = 3x + 4 and y = 3x + 7 are parallel because their slopes are the same (3).
The graphs of y = 2x - 5 and y = 5x - 5 are neither parallel nor perpendicular because their slopes are not the same (2 and 5).
The graphs of y = 3/5x - 3 and 5y = 3x - 10 are neither parallel nor perpendicular. The first equation is not in slope-intercept form, and the second equation is not in standard form.
The graphs of y = 7x + 2 and x + 7y = 8 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.
The graphs of y = -4x + 1 and 4y = x + 3 are perpendicular because the product of their slopes is -1.
The graphs of y = -1/3x + 2 and y = 3x - 5 are neither parallel nor perpendicular. The slopes are -1/3 and 3, which are not the same, so the lines are not parallel, and their product is not -1, so the lines are not perpendicular.
The graph of y = 4 is a horizontal line and the graph of 4y = 6 is not a function. So, they are neither parallel nor perpendicular.
The graphs of y = 5/6x - 6 and x + 5y = 4 are neither parallel nor perpendicular. The first equation is in slope intercept form, but the second equation is not.
Step-by-step explanation:
given that f(n)=8n-4 evaluate f with the indicate values a) f(5)
The value of the equation is f ( 5 ) = 36
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
f ( n ) = 8n - 4 be equation (1)
Now , when the value of n = 5 , we get
Substitute the value of n = 5 in the equation , we get
f ( 5 ) = 8 ( 5 ) - 4
On simplifying the equation , we get
f ( 5 ) = 40 - 4
f ( 5 ) = 36
Hence , the value of equation is f ( 5 ) = 36
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Solve this fraction and show your work
9/28 +29/70=?
Answer:
103/140
or
0.74
Step-by-step explanation:
9/28 +29/70
taking L.C.M of 29 and 70
= (9×5 + 29×2)/140
= (45 + 58)/140
= 103/140
= 0.74
Michael and Trevor are selling T shirts and sweatshirts with the school logo. Michael sells 10 Tshirts and 6 sweatshirts for $260. Trevor sells 5 Tshirts and 7 sweatshirts for $250. Write a system of equation to represent the situation. Using x for the price of tshirts and y for the price of sweatshirts. Solve the system of equations using elimination or substitution.
Answer:
x = 8
y = 30
Step-by-step explanation:
10x + 6y = 260
5x + 7y = 250
we can use the elimination method by multiplying the second equation by -2 to get:
-10x - 14y = -500
now we can add them together:
10x + 6y = 260
-10x - 14y = -500
the 'x' will be eliminated and we have -8y = -240
y = 30
plug 30 into either equation to solve for 'x':
10x + 6(30) = 260
10x + 180 = 260
10x = 80
x = 8