if we take 125 to be the 100%, what is 57 off of it in percentage?[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 125&100\\ 57&x \end{array}\implies \cfrac{125}{57}=\cfrac{100}{x}\implies 125x=5700 \\\\\\ x=\cfrac{5700}{125}\implies x = 45.6[/tex]
There are 125 people and 57 of the people have pets. What percent of people have pets.
First, we need to understand what the question is asking us to do. We know that there are 125 people altogether and only 57 of the people have pets. We are trying to figure out what percent of the people have pets.
The fraction [tex]\frac{57}{125}[/tex] is representing the 57 people who have pets out of all the people. To find what percent of people have pets, we have to change [tex]\frac{57}{125}[/tex] to a percent.
57 ÷ 125 = 0.456
0.456 × 100 = 45.6%
Therefore, 45.6% of people have have pets.
Which polynomial is in standard form?
Answer:
(C) 19x+6^2+2
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
edge 2021
The Finest Hour department store wants to run a special ad this week in The Country Times. It wants to run a half-page ad on Friday, and a full-page ad on Saturday and Sunday. How much will it cost the Finest Hour for the ads?
Sorry this took awhile.
So for Friday, it would be $550
Saturday, $895
Sunday, 1,095
So the total is $2540 if you add the numbers up. Hope this helps!
If y varies directly as x and y=4 when x=-2 find y when x=30
Answer:
Step-by-step explanation:
y=kx
4=k(-2)
k=-2
y=-2x
when x=30
y=-2*30=-60
Tickets to the concert cost $5.00 for adults and $2.50 for children. A group of 17 people went to the concert and paid $57.50 for tickets. How many adult tickets were purchased? How many children's tickets were purchased?
6 adults and 11 children.
In order to solve this problem we going to use linear equations.
A group of 17 people went to the concert. There are adults and children in that group x + y = 17 where x are adults and y are children. That group pay $57.50 for tickets, if tickets cost $5.00 for adults and $2.50 for children, then 5.00x + 2.50y = 57.50.
x + y = 17 ----------> y = 17 - x
Substituting the value of y in the equation 5.00x + 2.50y = 57.50:
5.00x + 2.50(17 - x) = 57.50 solving
x = 6
Substituting x = 6 in the equation x + y = 17
6 + y = 17 solving
y = 11
From a group of 17 people who went to the concert 6 are adults and 11 are children.
8s-10=27-(3s-7) What does “s” equal?
Answer:
s = 4
Step-by-step explanation:
Solve for s:
8 s - 10 = 34 - 3 s
Add 3 s to both sides:
8 s + 3 s - 10 = (3 s - 3 s) + 34
3 s - 3 s = 0:
8 s + 3 s - 10 = 34
8 s + 3 s = 11 s:
11 s - 10 = 34
Add 10 to both sides:
11 s + (10 - 10) = 10 + 34
10 - 10 = 0:
11 s = 34 + 10
34 + 10 = 44:
11 s = 44
Divide both sides of 11 s = 44 by 11:
(11 s)/11 = 44/11
11/11 = 1:
s = 44/11
The gcd of 44 and 11 is 11, so 44/11 = (11×4)/(11×1) = 11/11×4 = 4:
Answer: s = 4
4/3+6=1/4x
Solve the equation
Answer:
Step-by-step explanation:
cross multiply
4*4x=1*3+6
16x=9
x=9/16
what is the y=value of the vertex
y=-x squared -10x+24
Answer:
49
Step-by-step explanation:
y = -x² - 10x + 24
For a parabola ax² + bx + c, the vertex is at x = -b/(2a).
In this case, a = -1 and b = -10. So:
x = -(-10) / (2 * -1)
x = -5
The y coordinate is:
y = -(-5)² - 10(-5) + 24
y = -25 + 50 + 24
y = 49
Which pay rates are common ways employers pay employees?
commission
daily pay
hourly pay
quarterly pay
salary
Reset
help ASAP
Answer:
The employers pay their employees based on hourly rates, commission and salary.
Step-by-step explanation:
The employees get their pay based on hourly rates that can range from a minimum hourly rate of say $12 per hour to any maximum figure like $40 per hour.
The final salary is based on the numbers of hours worked multiplied by the hourly rate.
Secondly, the pays are also commission based. That is your base salary plus the commission.
The salary is typical in management positions. These are not hourly based but a lump sum pay.
So, the correct answers are : commission, hourly pay and salary.
Answer:
commission
hourly pay
salary
Step-by-step explanation:
PLATO USERS
Roxanne decides she's going to make cookies. Her recipe requires her to use 1 1/4 cup of sugar for each batch. Roxanne's Mom checked and they have 15 cup od sugar in the house. How many batches of cookies can Roxanne make with the sugar they have?
Answer:
i was a little unclear about your sugar amount..
Step-by-step explanation:
if the amount was 1 1/4 ( 1 cup and 1/4 cup) them the answer would be 12
12 x 1.25 = 15
if the sugar amount was just 1/4 cup of sugar the answer would be 60
.25 x 15 = 60
In the figure, mAB = 39° and mCD = 17°. The diagram is not drawn to scale.
What is the value of x?
A. 56°
B. 47.5°
C. 28°
D. 19.5°
It’s c which is 28 degree Celsius
The value of x will be equal to 28. The correct option is C.
What is intersecting chord theorem?'The intersecting chords theorem is a statement that describes a relation of the four-line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.'
According to the given problem,
Given,
AB = 39CD = 17We know, according to intersecting chords theorem,
⇒ x = [tex]\dfrac{CD + AB}{2}[/tex]
⇒ x = [tex]\dfrac{56}{2}[/tex]
⇒ x = 28
Hence, we can conclude, that the value of x is 28.
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Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?
5,–1, –7, –13, –19
Answer:
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
Step-by-step explanation:
The terms of the sequence are:
[tex]5,-1,-7,-13,-19[/tex]
The first term of this sequence is [tex]f(1)=5[/tex].
There is a constant difference among the terms.
This constant difference can determined by subtracting a previous term from a subsequent term.
[tex]d=-1-5=-6[/tex]
The general term of this arithmetic sequence is given recursively by [tex]f(n)=f(n-1)+d[/tex]
We substitute the necessary values to obtain:
[tex]f(n)=f(n-1)+-6[/tex]
Or
[tex]f(n)=f(n-1)-6[/tex], where [tex]f(1)=5[/tex] and [tex]n\:>\:1[/tex]
Answer:
C
Step-by-step explanation:
Which equation represents a proportional relationship that has a constant of proportionality equal to 4/5
A) y=x+4/5
B) y=4/5x
C) xy = 4/5
D) x+y=4/5
Answer:
Option B) y=4/5x
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
we have that
case A) y=x+4/5
The line does not passes through the origin, is not a proportional relationship
case B) y=(4/5)x
The line passes through the origin ---->represents a proportional relationship
The slope m is equal to the constant of proportionality k
The slope m=4/5
therefore
The line y=4/5x
Represents a proportional relationship that has a constant of proportionality equal to 4/5
case C) xy=4/5
Represent an inverse variation is not a proportional relationship
case D) x+y=(4/5)
The line does not passes through the origin, is not a proportional relationship
Answer:
The Answer is B.
Step-by-step explanation:
Trust me .
7. The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F. Write and solve an equation to
find the decrease in temperature
Answer:
The equation is equal to 78°-x=56°
The decrease in temperature is 22°
Step-by-step explanation:
Let
x-----> the decrease in temperature
we know that
The equation that represent this situation is equal to
78°-x=56°
Solve for x
x=78°-56°
x=22°
Answer:
The required equation is [tex]78^\circ F-t=56^\circ F[/tex]
The decrease in temperature is 22°F.
Step-by-step explanation:
Given : The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.
To find : Write and solve an equation to find the decrease in temperature ?
Solution :
We have given that temperature is dropped i.e. there is decrease in teh temperature.
Let the decrease in the temperature be 't'.
According to question,
The temperature in Springfield at 10:00 a.m. was 78°F. During the day, it dropped to 56°F.
i.e. the required equation is [tex]78^\circ F-t=56^\circ F[/tex]
Solve,
[tex]t=78^\circ F-56^\circ F[/tex]
[tex]t=22^\circ F[/tex]
The decrease in temperature is 22°F.
A cone-shaped dispenser is filled with cereal. The cone has a radius of 1.5 inches and a height of 5 inches. Which measurement is closest to the volume of cereal that the cone-shaped dispenser holds?
Possible Answers:
A - 3.75
B - 11.78
C - 141.37
D - 47.12
Answer:
Option B. [tex]11.78\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3} \pi r^{2}h[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]h=5\ in[/tex]
substitute
[tex]V=\frac{1}{3} \pi (1.5)^{2}(5)[/tex]
[tex]V=3.75\pi\ in^{3}[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]V=3.75(3.14)=11.78\ in^{3}[/tex]
if f(x)=x^2 - 12, solve for f (x+4)
Answer:
f(x + 4) = x² + 8x + 4Step-by-step explanation:
Instead of x substitute (x + 4) to f(x) = x² - 12
f(x + 4) = (x + 4)² - 12 use (a + b)² = a² + 2ab + b²
f(x + 4) = x² + 2(x)(4) + 4² - 12
f(x + 4) = x² + 8x + 16 - 12
f(x + 4) = x² + 8x + 4
Brett is paid $18.95 per hour with time and a half for overtime. What will his gross pay be for a pay period in which he worked 42 hours one week and 36 hours the next week for a total of 78 hours?
The gross pay will be $1496.78
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Brett is paid $18.95 per hour.
For 0 to 40 hours a week,
For any hours over 40, Brett makes
= 1.5 ($18.95)
= $28.425/hour
In Week 1: 40 hours x $18.95/hour = $758
2 hours x $28.425/hour = 56.85
Week 2: 36 hours x $18.95/hour = 682.2
So, total pay= 758 + 56.58+ 682.2 = $1496.78
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Final answer:
Brett's gross pay for working 42 hours one week and 36 hours the next, for a total of 78 hours, is $1495.05, which includes 2 hours of overtime pay.
Explanation:
Brett is paid an hourly wage of $18.95, with overtime paid at 1.5 times his regular rate. To calculate Brett's gross pay for the two-week pay period where he worked 42 hours one week and 36 hours the next week, we have to account for the fact that he worked 2 hours of overtime in the first week (since he worked more than 40 hours).
Step-by-Step Calculation
Regular hours for two weeks: 40 hours + 36 hours = 76 hours.Overtime hours for the first week: 42 hours - 40 hours = 2 hours.Calculate regular pay: 76 hours x $18.95/hour = $1438.20.Calculate overtime pay: 2 hours x ($18.95/hour x 1.5) = $56.85.Add regular and overtime pay: $1438.20 + $56.85 = $1495.05.Brett's gross pay for the 78 hours worked would be $1495.05.
What is the value of -6x3-y2-3xy if x=-2 and y=4
The answer is:
The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.
Why?To solve the problem, we need to evaluate both variables for the given values:
[tex]x=-2[/tex]
and
[tex]y=4[/tex]
So, we are given the expression:
[tex]-6x^{3}-y^{2}-3xy[/tex]
Then, evaluating the given values for both variables, we have:
[tex]-6*(-2)^{3}-(4)^{2}-3*(-2)*(4)=(-6*-8)-(16)+24=48-16+24=56[/tex]
Hence, we have that the answer is:
The value of the given expression evaluated with x equals to -2 and y equals to 4, is equal to 56 units.
Have a nice day!
Answer:
The value of given expression = 56
Step-by-step explanation:
It is given an expression in variable x and y
-6x³ - y² - 3xy
To find the value of given expression
Let expression be,
-6x³ - y² - 3xy
When x = -2 and y =4
-6x³ - y² - 3xy = -6(-2)³ - 4² - (3 * -2 * 4)
= -6*-8 - 16 + 24
= 48 - 16 + 24
= 56
Therefore the value of given expression is 56
john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80. How much did the pay for each burger and order of fries?
Answer:
They paid $2.85 for each burger and $1.8 for each order of fries
Step-by-step explanation:
It will be solved simultaneously,
let x represent burger and y represent fries
John's order gives the first equation
3x + 2y = 12.15 ........(1)
Emily's order gives the second equation
4x + 3y = 16.80 ..........(2)
multiply equation (1) by 3 and equation (2) by 2 so as to eliminate y
9x + 6y = 36.45 ....... (3)
8x + 6y = 33.6 ........... (4)
subtract equation (4) from (3)
9x - 8x + 6y -6y = 36.45 - 33.6
x = 2.85
substitute x= 2.85 in equation (1)
3(2.85) + 2y = 12. 15
8.55 + 2y = 12.15
2y = 12.15 -8.55
2y = 3.6
y = 1.8
Answer:
Cost of burger = $2.85 and Cost of fries = $ 1.80.
Step-by-step explanation:
Given : john order 3 burgers and 2 fries for $12.15. Emily bought 4 burgers and 3 fries for $16.80.
To find : How much did the pay for each burger and order of fries.
Solution : We have given 3 burgers and 2 fries for $12.15.
Let the cost of 1 burger = x .
Let the cost of 1 Fries = y .
3 x + 2 y = $12.15 ------(1)
4 x + 3 y = $16.80-----(2)
On multiplying (i) by 4 and (ii) by 3 and subtracting the equation .
12x + 8y = $48 .60
(-)12x +(-) 9y = (-)$50 .40
_____________
0 -y = -$ 1.80
y = $ 1.80.
3x + 2(1.80) = $12.15 .
3x + 3.60 = 12.15
3x = 12.15 - 3.60
3x = 8.55
On dividing both sides by 3.
x = $2 .85
Therefore, Cost of burger = $2.85 and Cost of fries = $ 1.80.
Write the fraction 72/81
in simplest form.
Answer: 8/9
Hope it helped!
Answer:
8/9
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 72 and 81 is 9
72 ÷ 9
81 ÷ 9
= 8/9
surface area of a pyramid. The base is a square with sides 4 inches long. the other faces are isosceles triangles. the ratio of the height of each triangle to its base is 3:2. Give the base length and the height of each triangular face
Answer:
Base of each triangular face = 4 inches
Height of each triangular face = 6 inches
Step-by-step explanation:
The length of each side of the square base is the base of each isosceles triangle forming the pyramid.
We know from our problem that the ratio of the height of each triangle to its base is 3:2, so [tex]\frac{height}{base} =\frac{3}{2}[/tex]. We also know that the base is a square with sides 4 inches long, since the bade of the square is the base of the isosceles triangle, [tex]base=4[/tex].
Replacing the value of the base in our proportion:
[tex]\frac{height}{base} =\frac{3}{2}[/tex]
[tex]\frac{height}{4} =\frac{3}{2}[/tex]
Multiply both sides by 4
[tex]\frac{height}{4}*4 =\frac{3}{2}*4[/tex]
[tex]height=\frac{3*4}{2}[/tex]
[tex]height=\frac{12}{2}[/tex]
[tex]height=6[/tex]
We can conclude that he base of each isosceles triangle is 4 inches and its height is 6 inches.
at a basketball game at team made 55 successful shots they were a combination of one and two point shots the team scored 92 points in all right and solve a system of equations to find out the number of each type of shot
Final answer:
To determine the number of one-point and two-point shots made by a basketball team that scored 92 points from 55 shots, set up a system of equations. Solve the system to find that the team made 18 one-point shots and 37 two-point shots.
Explanation:
Finding the Number of One-Point and Two-Point Shots
Let's define x as the number of one-point shots and y as the number of two-point shots. We then have the following system of equations based on the information provided:
x + y = 55 (Total number of successful shots)
1x + 2y = 92 (Total points scored)
To solve for x and y, we can use either substitution or elimination methods.
Using substitution:
Solve the first equation for x: x = 55 - y.
Substitute x in the second equation: 1(55 - y) + 2y = 92.Simplify and solve for y: 55 - y + 2y = 92, which simplifies to y = 37.Substitute y back into the first equation to find x: x = 55 - 37 = 18.The team made 18 one-point shots and 37 two-point shots.
Classify the system of equations
- 1/2x = -6 - y
3+y= 1/2x + 4
(2 points, 1 for work shown, 1 for correct classification with reasoning)
Answer: Inconsistent.
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Solve for y from each equation:
Equation 1:
[tex]-\frac{1}{2} x = -6 - y\\\\y-\frac{1}{2} x = -6\\\\y=\frac{1}{2} x-6[/tex]
Equation 2:
[tex]3+y= \frac{1}{2} x + 4\\\\y= \frac{1}{2} x + 4-3\\\\y= \frac{1}{2} x+1[/tex]
A system of equations can be classified by its number of solutions.
You can observe that the slopes of both equations are the same but the y-intercepts are different, then these lines are parallel, which means that they do not intersect.
By definition, when to lines are parallel there is NO SOLUTION and the system is classified as "Inconsistent".
After eliminating radicals, what quadratic equation can you solve to find the potential solutions of sqrt 2x+3 - sqrt x+1 = 1
Answer:
Step-by-step explanation:
We have given:
√2x+3 - √x+1 = 1
First of all isolate the square root of the left hand side:
√2x+3 = √x+1 +1
Now take square on both sides.
(√2x+3)^2 = (√x+1 +1)^2
Open the R.H.S by squaring formula.
∴(a+b)^2 = a^2+2ab+b^2
2x+3 = (√x+1)^2 + 2(√x+1)(1)+(1)^2
2x+3 = x+1 +2√x+1 +1
2x+3 = x+2 +2√x+1
Combine the like terms:
2x-x+3-2 = 2√x+1
x+1 = 2√x+1
Take square on both sides
(x+1)^2 = (2√x+1)^2
x²+2x+1 = 4x+4
x²+2x-4x+1-4 = 0
x²-2x-3 = 0
Now solve the quadratic equation:
a = 1 , b= -2 , c = -3
x = -b+/-√b²-4ac/2a
x = -(-2)+/-√(-2)² - 4(1)(-3) / 2(1)
x = 2 +/- √4+12 / 2
x = 2+/- √16/2
x = 2+/- 4 /2
x = 2+4/2 , x = 2-4/2
x = 6/2 , x = -2/2
x = 3 , x = -1
The solutions we get is (3, -1).
Answer:
Quadratic Equation: x²-2x-3 = 0
Solutions (Next Question): (3, -1)
Step-by-step explanation:
Absor201 is correct! (look at the BOLDED text in their answer)
the length of a slide at a water park is 50 feet from the top of the slide to ground level the top of the slide is 20 feet above the ground what is the approximate measure of the angle formed by the top of the slide and vertical support
Answer:
66
Step-by-step explanation:
cos 0=20/50
The approximate measure of the angle formed by the top of the slide and the vertical support is approximately 21.8 degrees.
In trigonometry, the tangent function can help us find the angle in a right-angled triangle. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case, the side opposite the angle is the height of the slide (20 feet), and the adjacent side is the length of the slide (50 feet).
Now, we can use the tangent function to find the angle (θ):
tan(θ) = Opposite / Adjacent
tan(θ) = 20 feet / 50 feet
tan(θ) = 0.4
To find the value of θ, we can take the inverse tangent (also known as arctan or tan⁻¹) of 0.4:
θ ≈ arctan(0.4) ≈ 21.8 degrees
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2 qt/min= how many gal/s
The flow rate is 2 quarts per minute. There are 4 quarts in a US gallon, so 2 quarts divide 4 quarts per US gallon = 0.5 gallons per minute There are 60 seconds in a minute, so the flow rate is 0.5 gallons per minute divide 60 seconds per minute = 0.0083 gallons per second
Converting 2 quarts per minute to gallons per second requires the use of two conversion factors. First, quarts are converted to gallons by dividing by 4. Then, minutes are converted to seconds by dividing by 60. After performing these steps, it is found that 2 quarts per minute is approximately equal to 0.00833 gallons per second.
Explanation:The student is asking to convert a flow rate from quarts per minute to gallons per second. There are a few fundamental conversions you need to use to find the answer. Firstly, remember that 1 gallon (gal) is equivalent to 4 quarts (qt). So, to convert the quarts to gallons, divide the quarts by 4. Secondly, there are 60 seconds in a minute; thus, you have to convert the minutes to seconds by dividing by 60.
Let's go step-by-step:
Convert quarts to gallons: 2 quarts/minute ÷ 4 = 0.5 gallons/minuteConvert minutes to seconds: 0.5 gallons/minute ÷ 60 = 0.00833 gallons/secondTherefore, 2 quarts per minute is approximately equal to 0.00833 gallons per second.
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Hillary joins a gym. She pays $15 per month plus $13.75 for each personal training session she does. If her monthly bill is $125, how many personal training sessions did she get that month?
Subtract the monthly fee from the total, then divide by the price of each session.
125 - 15 = 110
110 / 13.75 = 8
She got 8 sessions.
15 points!!!
Two right triangles are shown below.
Which statement is true?
There is a dilation centered at the origin with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at (-2,0) with scale factor 2 transforming triangle I into triangle III.
There is a dilation centered at a point off of the x-axis transforming triangle I into triangle III.
There is no dilation transforming triangle I into triangle III.
Answer:
The correct option is 4.
Step-by-step explanation:
If a figure it dilated by scale factor k, then the image and preimage are similar figures and their corresponding sides are proportional.
In triangle I, the base of the triangle is 1 unit and length of the perpendicular is 1 units.
In triangle II, the base of the triangle is 1 unit and length of the perpendicular is 2 units.
[tex]\frac{1}{1}\neq \frac{1}{2}[/tex]
The corresponding sides are not proportional. It means both triangles are not similar. So, there is no dilation transforming triangle I into triangle II.
Therefore the correct option is 4.
Answer:
There is no dilation transforming triangle I into triangle II.
Step-by-step explanation:
What is the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares?
Answer:
200Step-by-step explanation:
The square of the sum of the first five positive integers:
(1 + 2 + 3 + 4 + 5)² = 15² = 225
The sum of the first positive perfect square:
1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55
225 - 55 = 200
The positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170. This is obtained by taking the sum of first five numbers, squaring the sum and subtracting the sum of first five perfect squares.
Calculate the positive difference:The sum of first five positive integers = 1+2+3+4+5 = 15
Square of the sum of the first five positive integers = 15² = 225
The sum of the first five positive perfect squares =1²+2²+3²+4²+5²
=1+4+9+16+25
=55
The positive differenece = 225-55=170
Hence the positive difference between the square of the sum of the first five positive integers and the sum of the first five positive perfect squares is 170.
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Two positive integers have a sum of 10 and a product of 21. What are the integers?
Answer:
3 and 7Step-by-step explanation:
[tex]x,y-\text{positive integers}\\\\\text{The system of equations:}\\\\\left\{\begin{array}{ccc}x+y=10&\text{subtract}\ y\ \text{from both sides}\\xy=21\end{array}\right\\\\\left\{\begin{array}{ccc}x=10-y&(1)\\xy=21&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(10-y)(y)=21\qquad\text{use the distributive property}\ a(b-c)=ab-ac\\\\10y-y^2=21\qquad\text{subtract 21 from both sides}\\\\-y^2+10y-21=0\qquad\text{change the signs}\\\\y^2-10y+21=0\\\\y^2-3y-7y+21=0\\\\y(y-3)-7(y-3)=0[/tex]
[tex](y-3)(y-7)=0\iff y-3=0\ \vee\ y-7=0\\\\y-3=0\qquad\text{add 3 to both sides}\\\\y=3\\\\y-7=0\qquad\text{add 7 to both sides}\\\\y=7\\\\\text{Put the value of}\ y\ \text{to (1):}\\\\x=10-3=7\ or\ x=10-7=3[/tex]
5(x + 2)
F(x) -
y - 11x + 7)
Answer:
Problem:
Solve x+y=7;x+2y=11
Steps:
I will try to solve your system of equations.
x+y=7;x+2y=11
Step: Solvex+y=7for x:
x+y+−y=7+−y(Add -y to both sides)
x=−y+7
Step: Substitute−y+7forxinx+2y=11:
x+2y=11
−y+7+2y=11
y+7=11(Simplify both sides of the equation)
y+7+−7=11+−7(Add -7 to both sides)
y=4
Step: Substitute4foryinx=−y+7:
x=−y+7
x=−4+7
x=3(Simplify both sides of the equation)
Answer:
x=3 and y=4