The value of 'x' and 'y' is '1' and '3' , respectively.
Substitution method :The substitution method is the algebraic method to solve simultaneous linear equations.
The first step in the substitution method is to find the value of any one of the variables from one equation in terms of the other variable.
Lets solve the given linear equations:
7x − 2y = 1 ... eq. (1)
3x + 4y = 15 ... eq. (2)
By equation 1 we got,
x = (1 + 2y)/7
Now, we will put x = (1 + 2y)/7 in equation 2,
3x + 4y = 15
3 [(1 + 2y)/7] + 4y = 15
3/7 × (1 + 2y) = 15 - 4y
3(1 + 2y) = 7(15 - 4y)
3 + 6y = 105 - 28y
6y + 28y = 105 - 3
34y = 102
y = 102/34
y = 3
Now, put the value y =3 in equation 1,
7x - 2y = 1
7x - (2×3) = 1
7x - 6 = 1
7x = 1 + 6 = 7
7x = 7/7
x = 1
Hence, the value of x is 1 and y is 3.
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Evaluate a + b² if a = -3 and b = 6.
117
Answer: 33
Step-by-step explanation:
(-3)+(6)^2
-3+36
33 (Answer)
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
√x² - y²
When x = 3and y = -6, the value of the expression is
Reset
-33 is the value of √x² - y² at x = 3 and y = -6.
The expression given in the question is √x² - y² and we have to find the value of this expression when the value of x is 3 and the value of y is -6.
In order to evaluate √x² - y² simply put x = 3 and y = -6 and then solve accordingly.
Let's proceed to solve the expression,
√x² - y²
at x = 3 and y = -6. we have
= √3² - (-6)²
= √9-36
= 3-36
= -33
⇒√x² - y² = -33
∴ On solving, √x² - y² for x = 3 and y = -6 we get -33 as its evaluation.
Hence, -33 is the required answer.
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In a bag, there are numbered tiles 1 through 10. You will pick a tile, replace it, then pick another one. Find the following probabilities.
P (1, the 3)
P ( odd, then number less than 4 )
P ( even, then odd )
Please help, this paper is due tomorrow and I have no idea what I'm doing!
Answer:
Wait, can you explain the answer choices, I don't understand them.
Step-by-step explanation:
IT RAINS 15 DAYS IN JANURAY WRite the ratio of rainiy days to dry days
Answer:
3:9 6:15 14:21 15:35 all of these should work
Given the linear functions f(x) = x-3 and g(x) = -2x + 4, determine (f g)(x).
O(f-g)(x) = -2x - 12
O(1-g)(x) = -2x² - 12
O(1-g)(x) = -2x2 - 2x - 12
O(f g)(x) = -2x2 + 10x - 12
The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?
w ≤ 10 – l
2l + 2w ≥ 62
w ≤ 10 – l
2l + 2w > 62
w ≤ l – 10
2l + 2w ≥ 62
w ≤ l – 10
2l + 2w > 62
the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
Let the length of the pool be x.
So, ATQ, the width will be represented by the inequality:
x - 10 ≥ width
w ≤ x - 10
w ≤ l - 10
Also, it is given that, the perimeter of the pool is more than 62 m
So, we get that:
P > 62
Also, we know that:
P = 2 l + 2 w
So, we get that:
2 l + 2 w > 62.
Therefore, the system of inequalities that represents the possible length in meters, l, and the possible width in meters, w, of the pool is given as w ≤ l - 10 and 2 l + 2 w > 62.
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Answer:
D
Step-by-step explanation:
i’m pretty sure
Stephanie is a taxi driver. She rents her taxi for $300/week. She feels she can take in $120/day in fares. Let D be the number of days she drives her taxi in a week and T be the total earnings she expects after subtracting the rental charge.
a. Identify four ordered pairs (D,T).
b. Write an equation that gives T as a function of D.
c. What is the most she can earn in a year at this rate?
Answer: a. (0, -300), (1, -180), (2, -60), (7, 540)
b. T=120D-300
c. $28080
Step-by-step explanation:
a. T=120D-300 ==> per week
D=0: T=120(0)-300
D=0: T=-300 ==> (0, -300)
D=1: T=120(1)-300
D=1: T=120-300
D=1: T=-180 ==> (1, -180)
D=2: T=120(2)-300
D=2: T=240-300
D=2: T=-60 ==> (2, -60)
D=7: T=120(7)-300
D=7: T=840-300
D=7: T=540 ==> (7, 540)
b. T=120D-300
c. T=120(7)-300
T=840-300
T=$540 per week
1 year = 52 weeks
540*52=$28080
A gardener can trim all the bushes on the Green's property
in 5 hours. If his assistant helps him, they can complete the job
in 4 hours. How long would it take the assistant to do the job
alone?
(In hours)
It would take the assistant 20 hours to do the job alone.
How to determine the valueFrom the information given, we have that;
The gardener trims for 5 hours aloneThe gardener and assistant trims for 4 hoursLet the gardener be x
His assistant be y
So,
y = 1/ 5
x + y = 1/ 4
Substitute the value
x = 1/ 4 - 1/ 5
Find the LCM
x = 1 / 20
Take the reciprocal
x = 20 hours
Thus, it takes the assistant 20 hours to do the job alone.
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the points (4,1), (2.-2), and (-3,-3) are vertices of a polygon. What is the best name of the polygon?
Answer:
A Triangle
Step-by-step explanation:
Since the three points are not collinear, the vertices form a triangle.
what is the value of 100 3/2 ?
Answer:
101 1/2
3/2=1 1/2
100+1 1/2= 101 1/2
23. MATHEMATICAL CONNECTIONS Two lines are cut by
a transversal. Is it possible for all eight angles formed
to have the same measure? Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
If you use only perpendicular lines, all angles should be exactly 90 degrees
What is an equation of the line that passes through the points (−1,−7) and (−8,0)?
The equation of the line that passes through the points is y = -x - 8
What is an equation of the line that passes through the points?The points are given as:
(−1,−7) and (−8,0)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
So, we have
m = (0 + 7)/(-8 + 1)
This gives
m = -1
The equation of the line that passes through the points is then calculated as
y = m(x - x1) + y1
So, we have
y = -1(x + 8) + 0
This gives
y = -x - 8
Hence, the equation of the line that passes through the points is y = -x - 8
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Rafael is building a frame in the shape of a square. The area of the frame is 40 square inches. Find the length of the side of the frame to the nearest inch.
The length of the side of the frame will be 6.33 to the nearest inch.
What is the area of the square?All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square.
Then the area of the square would be;
Area of the square = a² square units
We have been given that Rafael is constructing a square-shaped frame. And the frame has a 40 square inches surface area.
A = a²
40 = a²
a = √40
a = 6.33 inches
Hence, The length of the side of the frame to the nearest inches will be 6.33 to the nearest inch.
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need help with this work it is 6th grade
Answer:
1/4
Step-by-step explanation:
You jumped rope of 1/3 of 3/4 hour.
In math, "of" usually means times.
1/3 of 3/4 hour = 1/3 × 3/4 hour = (1 × 3)/(3 × 4) hour = 3/12 hour = 1/4 hour
Answer: 1/4
how do you devide triple diget numbers?
For example:
240 ÷ 160
estimate the solution to the following system of equations by graphing. 3x + 5y= 14. 6x - 4y=9
the estimated solution for the equations 3 x + 5 y = 14 and 6 x - 4 y = 9 is (5/2, 4/3).
We have the equations:
3 x + 5 y = 14
6 x - 4 y = 9
The exact solution is the point (2.41, 1.36)
1.(5 / 2, 4 / 3)-----> (2.5, 1.33)--------> is the best approximation
2.(4 / 3, 5 / 2)------> (1.33, 2.5)
3.(7 / 3, 7 / 2)------> (2.33, 3.5)
4.(- 5 / 2,-7 / 5)----> (- 2.5, - 1.4)
The estimate solution is (5/2, 4/3).
Therefore, the estimated solution for the equations 3 x + 5 y = 14 and 6 x - 4 y = 9 is (5/2, 4/3).
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How many liters would a 5 kilolitre JoJo tank hold
Answer:
5000 litres
Step-by-step explanation:
1 kilolitre is 1000 litres
Answer: The tank would hold 5000 Liters
Halle la razón aritmética y geométrica de 91 y 7.
It should be noted that the ratio of 91 to 7 will be 13:1.
How to calculate the ratio?It should be noted that when you want to calculate a ratio, you have to look at the common factor that the figures have.
In this case, the common factor that 91 and 7 has is 7
Therefore, the ratio will be:
= 91/7
= 13/1
In conclusion, the ratio is 13:1
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can u pls help me with my ixl
The dimensions of a basketball court are shown below. Suppose a player throws the ball from a corner to a teammate standing at the center of the court. a. If center court is located at the origin, find the ordered pair that represents the location of the player in the bottom right corner b. find the distance that the ball travels
The 94 ft. by 50 ft dimensions of the court obtained from a similar question posted online, gives;
a. The ordered pair representing the location of the player in the bottom right corner is (47, -25)
b. The distance traveled by the ball obtained using Pythagorean theorem, is approximately 53.2 feet.
How can Pythagorean theorem be used to find the distance the ball travels?The possible dimensions of a rectangular court obtained from a similar question posted online are;
Length of the basketball court = 94ft.
Width of the basketball court = 50 ft.
From the question, we have;
Location of the court center = The origin of a coordinate plane
a. The ordered pair that represent the location of a player in the bottom right corner is found as follows;
Let (x, y) represent the coordinates of the bottom right corner of the court, we have;
Horizontal distance from the center of the court (the origin) to the right boundary of the court, x = (94 ft.)/2 = 47 ft.
Vertical distance from the center to bottom of the court, y = (50 ft.)/2 = 25 ft.
Following the convention of points to the right and above the origin being positive, while points below the origin are negative, we have;
The ordered pair (the coordinates of the player) that represents the location of the player in the bottom right corner is therefore;
(x, y) = (47, -25)b. The distance, d, that the ball travels is given by Pythagorean theorem as follows;
d = √((47 - 0)² + ((-25) - 0)²) = √(2834) ≈ 53.2
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Three lakes lost water during a drought. lake jensen lost one sixth of its water, lake parlow lost 26% of its water, and lake stockton lost thirty three two hundredths of its water. which lake lost the least amount of water?
If three lakes lost water during a drought, lake Jensen lost one-sixth of its water, lake Parlow lost 26% of its water, and lake Stockton lost thirty-three two-hundredths of its water, then the lake that lost the least amount of water is lake Stockton.
The lake that lost the least amount of water can be determined by converting the amounts lost by each of the lakes into percentage form.
As lake Jensen lost one-sixth of its water, it can be written in percentage form as,
Lake Jensen = 1/6 × 100 = 100/6 = 16.67 %
As given, Lake Parlow lost 26%
Lake Parlow = 26%
As Lake Stockton lost thirty-three two-hundredths, it can be written in percentage form as,
Lake Stockton = 33/200 × 100 = 0.165 × 100 = 16.5 %
Thus, the least percentage of water lost is 16.5% by lake Stockton.
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is shown below. Find the value of f(-4)
======================================================
Explanation:
Start at -4 on the x axis.
Draw a vertical line until reaching the curve.
Then draw a horizontal line until reaching the y axis.
You should arrive at y = -5. This tells us f(-4) = -5
The input x = -4 leads to the output y = -5
The point (-4, -5) is on the graph. This is the highest point, so it's the vertex of the V shape.
See the diagram below.
Given the figure below, find the values of x and z.
By using the property of vertically opposite angles the value x= 4 and the angle z = 78°
What are vertically opposite angles?
Vertical opposite angles are angles made at the intersection of two lines, these are non adjacent angles that are opposite to each other.
Vertical opposite angles are equal to each other.
In the given figure (5x + 82)° and (11x + 58)° are vertically opposite angles.
(5x + 82)° = (11x + 58)°
5x + 82 = 11 x + 58
82- 58 = 11x - 5x
24 = 6x
x = 24 /6 = 4
Then (5x+82) = (5(4) +82)= 102
(5x + 82)° and z° both are angles on same line therefore their sum will be 180°
(5x+82) +z =180
102+z=180
z= 180-102 = 78
Therefore, the value x= 4 and the angle z = 78°.
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I will give brainliest to person who answers and double points!!!!
Answer:
x=17 3y=13+10-3
x=17y=20
Step-by-step explanation:
answer to the questions
Answer:
x = 3 y = 46
Step-by-step explanation:
8x+13 = 9x+10
-8x -8x
13 = x+10
-10 -10
3 = x
180-37 = 143
3y+5 = 143
-5 -5
3y = 138
/3 /3
y = 46
Can someone help me solve all of the questions on this pdf?
Answer:
sure y not
Step-by-step explanation:
basta alam ko y not hindi
isiah copeland sells tennis equipment. he is guaranteed a minimum salary of $1,500 per month plus 5.75% of his total sales.
The correct answer would be "A. $2,075 = $1,500 + (.0575*s)" total sales.
What is sales?A sale is a deal in which two or more parties trade products or services for cash or other assets, usually between a buyer and a seller. It is an agreement between a buyer and seller on the price of a security and the delivery of the security to the buyer in exchange for the agreed-upon compensation constitutes a sale in the financial markets. The transaction is not regarded as a sale if the product or service in issue is given by one party to the other without receiving payment, but rather as a gift or donation.
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What is Missing?
Fill in the circles with the missing information. Then place the area on the spaces provided as both a sum
and a product. 4 points each
21. Area as sum = 12x + 60
Area as Product = 12(x + 5)
22. Area as sum = 5x + 20
Area as Product = 5(x + 4)
How to Find the Area of a Rectangle as a Sum and as a Product?As a product, we can multiply the height and the base of the rectangle.
As a sum, we can find the area finding the sum of the areas of each pieces of the rectangle.
The missing pieces of that will fill into the circles is shown in the diagram attached below. Therefore, we would have the following:
21. Area as sum = 12x + 60
Area as Product = 12(x + 5)
22. Area as sum = 5x + 20
Area as Product = 5(x + 4)
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A line with a slope of 1 passes through the point (6,8). What’s it’s equation in slope intercept form?
Step-by-step explanation:
using y=mx+c (equation of a line)
equation of one point form
y-y1=m(x-x1)
where y1=8,x1=6,m=1
y-8=1(x-6)
y-8=x-6
y=x-6+8
y=x+2
intercept form=2
or
y=mx+c where y=8,x=6,m=1
8=1(6)+c
8=6+c
8-6=c
2=c
or c=2
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Find the value of f(-5)
Answer:
y=3 or just put 3
Step-by-step explanation:
25 points plus brainliest
The largest integer is 0 (first option).
What is the largest integer?Integers are whole numbers. An integer is number that is not a fraction and not a decimal. Integers can either be positive, negative or zero. An example of an integer is 100, - 100 and 0.
An even number is a number that is divisible by 2 into two equal halves. An example is 2, 4, 6, 8. Consecutive even integers are whole even numbers that follow each other on the number line. An example is 2, 4, 6, 8.
If 0 is the largest number, the other three consecutive even integers would be : 0, -2, - 4, - 6. The sum of these numbers is -12.
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