To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system. Then we will calculate the solution to the modified system of equations and check if the solution is the same.
Explanation:To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system of equations (1,3). Then we will calculate the solution to the modified system of equations in which the first equation is replaced with the sum of the two equations. If the solution to the modified system is also (1,3), then we have shown that the modified system has the same solution.
Original system:
Equation 1: 2x + y = 5
Equation 2: x - 2y = -5
Substitute x = 1 and y = 3 into the original equations to check if it is a solution:
Equation 1: 2(1) + 3 = 5 => 2 + 3 = 5 => 5 = 5 (true)
Equation 2: 1 - 2(3) = -5 => 1 - 6 = -5 => -5 = -5 (true)
Hence, (1,3) is a solution to the original system of equations.
To create the modified system, we will sum equation 1 and a multiple of equation 2:
New equation 1: (2x + y) + k(x - 2y) = 5 + k(-5), where k is a constant
Expanding and simplifying the equation:
(2 + k)x + (1 - 2k)y = 5 - 5k
Let's substitute x = 1 and y = 3 into the modified equation to check if (1,3) is a solution:
(2 + k)(1) + (1 - 2k)(3) = 5 - 5k
2 + k + 3 - 6k = 5 - 5k
3 - 5k = 5 - 5k
3 = 5 (false)
Therefore, the modified system does not have the same solution as the original system, disproving the statement.
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Rewrite the given expression in the form 2^u where u is a constant or an algebraic expression.
1/2^5 = ? (Put the answer in exponential notation.)
To rewrite 1/2^5 in exponential notation, remember that 1/2^5 is the same as 2^-5. Therefore, 1/2^5 = 2^-5.
Rewrite the given expression in the form 2u where u is a constant or an algebraic expression.
To rewrite 1/25 in exponential notation, we need to understand that 1/25 is the same as (2-1)5. Using the property of exponents, we can rewrite this as 2-5, where -5 is the new exponent.
Therefore, 1/25 = 2-5, where u = -5.
The gear ratio describes the ratio of one gear's diameter to another gear in the same chain. The gear ratio between two specific gears is 3 to 2. If the diameter of the larger gear is 18 cm, what is the diameter of the smaller gear?
A. 24 cm B. 18 cm
C. 12 cm D. 6 cm
Sum or product of a nonzero rational number and an irrational number is always_____
A. rational,
B. irrational,
C. a repeating decimal,
D. a fraction
If RS//MN ,then the value of a is
Alicia cashed her paycheck and used half her earnings to take three friends to dinner. She spent $42.15 on dinner and she brought home more than $20.00. Write an inequality to represent the situation, using x to represent the amount of Alicia's paycheck.
Write the slope-intercept form of an equation of the line that passes through (2,-4) and (0,6)
we know that
the equation of the line in the slope-intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope of the line
b is the y-intercept of the line
Let
[tex]A(2,-4)\\B(0,6)[/tex]
Step [tex]1[/tex]
Find the slope of the line AB
the slope between two pints is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
substitute the values
[tex]mAB=\frac{(6+4)}{(0-2)}[/tex]
[tex]mAB=\frac{(10)}{(-2)}[/tex]
[tex]mAB=-5[/tex]
with the slope m and the point B find the value of b
[tex]B(0,6)[/tex]
[tex]6=-5*0+b[/tex]
[tex]b=6[/tex]
Find the equation of the line
[tex]y=mx+b[/tex]
[tex]y=-5x+6[/tex]
therefore
the answer is
[tex]y=-5x+6[/tex]
A box is in the shape of a right rectangular prism. The base of the box has an area of 15 square inches. The height of the box is 12 inches. What is the volume in cubic inches, of the box
The medicine capsule shown consists of a cylinder with a hemisphere at each end. The total length of the capsule is 15 millimeters. The diameter is 5 millimeters. Which choice is the best approximation of the total surface are of the capsule? Usa 3.14 to approximate pi.
Answer 236 square millimeters
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How does a reflection affect the properties of a two-dimensional figure ?
Therefore in two-dimensional figure reflection show mirror image of flipped
A reflection affect the properties of a two-dimensional figure.
What is the reflection?A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
In two dimensional figure reflection affects
and it is it gets mirrored or flipped.
Therefore in two-dimensional figure reflection show mirror image of flipped.
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I need desperate help
the expression (x+a)(x+b) cannot be written as
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
What is the distributive property?The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
Using distributive property, we get
x(x+b)+a(x+b)
= x²+bx+ax+ab
= x²+x(a+b)+ab
The expression (x+a)(x+b) can not be written as a(x+b) + x(x+b). Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The expression (x+a)(x+b) can not be written as
a) a(x+b) + x(x+b)
b) x² + (a+b)x + ab
c) x² + abx + ab
d) x(x+a) + b (x+a)
How do you calculate the volume of a cone when given the height and diameter? Describe the steps used to solve.
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
Answer:
Step-by-step explanation:
First find the radius by taking half the diameter. Use the radius to find the base area by using the formula for the area of a circle. Find the product of the base area and height, and then take one-third of the product.
A cylinder has a radius of 4 feet and a height of 3 feet. What is the volume of the cylinder to the nearest tenth 3. Use 3.14 to approximate π
Answer:
70Pi ft2
Step-by-step explanation:
ed2020
how can you tell if radicals are like radicals
Answer and step-by-step explanation:
Like radicals have the same root (square root, cubed root, etc.) and the same expression under the radical sign.
In order to determine if two radicals are like, simplify both and then check both the root and the expression under the radical sign.
The rabbit population in a certain area is 500% of last year's population. There are 900 rabbits this year. How many were there last year?
Answer:
180
Step-by-step explanation:
we got the same qustion and i just got this wrong
Which expression best estimates
What value should go in the empty box to complete the calculation for finding the product of 23.456 × 0.86? 23.456 times 0.86 gives two partial products. The first is 140736, and the second is unknown. 1,576,480 1,623,392 1,876,480 1,923,392
lugos and paschal each wrote an equation for the line that passes through (-3,2) and (6,8) lugos says the equation is y=2/3x+4 and paschal says the equation is 2x-3y=-12. who is correct? why do you say so?
The formula to find the perimeter of a regular polygon is P = n × s. This means that you multiply the number of sides times the length of each side. Which polygon will have the greatest perimeter? A. a hexagon with each side 3 cm B. a square with each side 5 cm C. a triangle with each side 7 cm D. a pentagon with each side 4 cm
A teacher would like to estimate the percentage of her students who play chess. Which method should the teacher use to select the sample?
A select every other student in her classes until she has selected a total of 30 students
B select all students who are currently in the chess club
C use a computer to randomly select 30 student IDs from all her students
D use a computer to randomly select 30 student IDs from all students
Answer:
the answer is C.
Step-by-step explanation:
since shes trying to find HER students D is wrong and since she needs a random amout of kids it doesnt make sense to choose a and since shes trying to find the percentage of her kids that play chess it would make sense to choose ppl who are already in the chess club.
Your school is 20 blocks east and 12 blocks south of your house. The mall is 10 blocks north and 7 blocks west of your house. You plan on going to the mall right after school. Find the distance between your school and the mall assuming there is a road directly connecting the school and the mall. One block is 0.1 mile. Round your answer to the nearest tenth of a mile.
East=X, West=-X, North=Y, South=-Y
Answer:3.623 miles
Step-by-step explanation:
Given
School is 20 blocks east and 12 blocks south
and mall is 10 blocks north and 7 block west.
There is a road directly connecting the school and the mall.
So distance between school and the mall is
[tex]=\sqrt{(20+12)^2+(10+7)^2}[/tex]
[tex]=\sqrt{32^2+17^2}[/tex]
[tex]=\sqrt{1024+289}[/tex]
=36.23 blocks
And 1 block is 0.1 mile so 36.23 blocks is 3.623 miles
In the diagram below, AC is perpendicular to BD. Find X.
Answer: The correct option is
(D) 17.5.
Step-by-step explanation: Given that in the diagram shown, AC is perpendicular to BD, where
[tex]m\angle BEC=(6x-15)^\circ,\\\\m\angle AED=(3y+12)^\circ.[/tex]
We are to find the value of x.
Since AC is perpendicular to BD and they are intersecting each other at the point E.
So, all the four angles made by this intersection are right angles.
That is, angle BEC is also a right angle.
Therefore, we get
[tex]m\angle BEC=90^circ\\\\\Rightarrow (6x-15)^\circ=90^\circ\\\\\Rightarrow 6x-15=90\\\\\Rightarrow 6x=105\\\\\Rightarrow x=\dfrac{105}{6}\\\\\Rightarrow x=17.5.[/tex]
Thus, the required value of x is 17.5.
Option (D) is CORRECT.
What is these answer
Can you Answer the question
A biologist wants to estimate the median width of over 200 oak trees in a forest. Ten trees were selected at random, and their widths, in centimeters, were recorded. 63, 59, 12, 43, 71, 35, 28, 52, 47, 26 What is the estimated median width of all oak trees in the forest? Enter your answer in the box.
Answer:
45
Step-by-step explanation:
The estimated median width of all oak trees in the forest is 45 centimeters.
How to calculate the median width?
To estimate the median width of all oak trees in the forest, we can use the sample of ten trees that were selected at random.
First, we need to order the sample from smallest to largest:
12, 26, 28, 35, 43, 47, 52, 59, 63, 71
The median is the middle value in the ordered list. In this case, there are ten numbers in the list, so the median is the average of the fifth and sixth numbers:
median = (43 + 47) / 2 = 45
Therefore, the estimated median width of all oak trees in the forest is 45 centimeters.
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Please help me!!! Zoom in on picture to read the other 2 questions. 1 questions if on 2 parts of the collage.
Ferris wheel is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270° about the origin?
Answer:
1. option A is correct i.e., [tex]\(90^{\circ}[/tex].
2. option B is correct.
3. the coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Step-by-step explanation:
1. The angle of rotation is [tex]\(90^{\circ}[/tex].
To calculate the angle of rotation we can use a protractor and measure the angle between two corresponding angles, using point C as a center.
2. Given: ΔPRS with coordinates P(-3,2), R(2,5) and S(0,0) is rotated through an angle of 270°, the new image will be as follows;
The formula for rotation through 270° is: (x,y) → (y,-x)
hence our image will be at point:
P(-3,2)→P'(2,3)
R(2,5)→R'(5,-2)
S(0,0)→S'(0,0)
from the above, the approximate image will be option B.
3. Given: Ferris wheel is drawn on a coordinate plane at the point P(30,0). The coordinates of the car after a rotation of [tex]\(270^{\circ}[/tex] is (0,-30).
Because the formula for rotation through 270° is: (x,y) → (y,-x).
So, point P(30,0)→P'(0,-30).
If you work for an hourly wage, your gross pay is a function of the number of hours that you work. If you earn $8 per hour, complete the following table:
Number of Hours
0
3
5
7
10
12
Gross Pay
If you were to plot the ordered pairs on a set of axes, in which quadrant would the domain and range of the function lie?
a.
8, 16, 24, 32, 40, 48; Quadrant I
b.
0, 24, 40, 56, 80, 96; Quadrant II
c.
8, 16, 24, 32, 40, 48; Quadrant II
d.
0, 24, 40, 56, 80, 96; Quadrant I
Answer:
D is the answer
Step-by-step explanation:
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Matt has a quiz every 6th day of class, and Meg has a quiz every 3rd day of class. When will they have a quiz on the same day?
The correct answer is:
The 6th day.
Explanation:
To solve this, we find the least common multiple (LCM) of 3 and 6. We find the prime factorization of each number:
3 = 3×1
6 = 2×3
We multiply the common factor, 3, by the uncommon factors, 2 and 1:
3×2×1 = 6
The LCM is 6; this means they will both have a quiz on the 6th day.
a cylinder is 8 inches high. The circumference of the base 6pi inches. Find the volume
How many sides does a regular polygon have if each exterior angle has a measure of 15 degrees? (Show work!!)