The method of substitution is a three step method to solve the equations. In this method , one equation for one of the variables is solved and in the first step.
The outcome is then substituted to the second equation in the second step for solving the equation.The value is re-substituted to the original equation to find the outcome in the third step.
On solving the equations by substitution method we get x=14 and y=-3
Calculation:Given equations:
[tex]\rm 2x+8y = 4[/tex] (1)
[tex]\rm x=-3y+5[/tex] (2)
On substituting [tex]x=-3y+5[/tex] in equation 1:
[tex]\begin{aligned}\rm 2(-3y+5)+8y&=4\\\\-6y+10+8y&=4\\\\2y+10&=4\\\\2y&=4-10\\\\ 2y &= -6\\\\y&=\dfrac{-6}{2}\\\\y&=-3\end[/tex]
Substituting [tex]\rm y=-3[/tex] in equation 2:
[tex]\rm x&=-3y+5\\\\x&=-3(-3)+5\\\\x=9+5\\\\x=14[/tex]
Therefore the values of x and y for the given equations is 14 and -3 respectively.
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How many times bigger is 7 billion than 700 million
Peyton has two pizzas each Pizza is cut into 10 equal slices she and her friends eat 14 slices what part of the pizzas did they eat write your answer as a decimal please help
If the sum of four consecutive odd integers is 208, what is the smallest of the four integers?
Choose the triangle that seems to be congruent to the given one
We are given a figure with composite triangles.
We need to find a congruent triangle to triangle ADB.
Two figures are congruent if their corresponding sides and angles are congruent.
We can see
AB congruent to AB
AD congruent to BC and
AC congruent to BD.
Therefore, triangle ADB is congruent to triangle BAC by Side Side Side (SSS) congruence theorem.A helicopter flies 200 miles against the wind in 2 hours, with the wind, it can fly 300 miles in the same amount of time. Find the speed of the helicopter in still air.
Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30" m∠ROT = 30 ° 27' 10" 31 ° 28' 10" 30 ° 28' 10"
Answer:
Third option 30° 28' 10"
Brainlist?
Step-by-step explanation:
m∠ROT, formed by adjacent angles m∠ROS (20° 15' 40") and m∠SOT (10° 12' 30"), measures 30° 28' 10" according to the Angle Addition Postulate.
Attached diagram.
To find the measure of angle ROT (m∠ROT), you can use the Angle Addition Postulate.
The Angle Addition Postulate states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those two angles.
Here m∠ROS and m∠SOT as adjacent angles forming m∠ROT.
m∠ROS = 20 degrees 15 minutes 40 seconds
m∠SOT = 10 degrees 12 minutes 30 seconds
To find m∠ROT, add the measures of m∠ROS and m∠SOT:
m∠ROT = m∠ROS + m∠SOT
First, add the degrees, then the minutes, and finally the seconds separately:
Degrees: 20 degrees + 10 degrees = 30 degrees
Minutes: 15 minutes + 12 minutes = 27 minutes
Seconds: 40 seconds + 30 seconds = 70 seconds
Now, simplify the seconds by converting any excess seconds into minutes:
70 seconds = 1 minute and 10 seconds
Now, add the minutes to the total:
27 minutes + 1 minute = 28 minutes
So, m∠ROT is:
30 degrees 28 minutes 10 seconds
Therefore, the measure of the angle m∠ROT = 30 degrees 28 minutes 10 seconds.
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The above question is incomplete, the complete question is:
Use the following diagram to complete the required information. m∠ROS = 20 deg 15' 40", m∠SOT = 10 ° 12' 30"
m∠ROT =
30 ° 27' 10"
31 ° 28' 10"
30 ° 28' 10"
Attached diagram.
which quadrant is (8, -1) in (A) | (B) || (C) ||| (D) ||||
What is the common difference between the elements of the arithmetic sequence below? -18, -22.5,-27,-31.5,-36
Answer:
-4.5
Step-by-step explanation:
What is the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5?
y = x – 8
y = x + 1
y = x + 1
y = x + 10
Answer:
[tex]y=\frac{3}{2}x+10[/tex]
Step-by-step explanation:
Given equation of line : [tex]2x + 3y = -5[/tex]
Standard form of equation of line = [tex]y=mx+c[/tex] ---A
Where m is the slope
Convert the given equation in standard form
[tex]2x + 3y = -5[/tex]
[tex] 3y = -5-2x[/tex]
[tex] y =\frac{-5}{3}-\frac{2}{3}x[/tex]
So, slope =[tex]m = -\frac{2}{3}[/tex]
If the two lines are perpendicular then the product of their slopes is -1
Let n be the slope of required equation of line
So, [tex]m \times n = -1[/tex]
[tex]-\frac{2}{3}\times n = -1[/tex]
[tex]n=\frac{3}{2}[/tex]
Substitute this value in A
[tex]y=\frac{3}{2}x+c[/tex] --B
Now we are given that the required perpendicular line passes through the point (–6, 1)
So, substitute (–6, 1) in B
[tex]1=\frac{3}{2}(-6)+c[/tex]
[tex]1-(\frac{3}{2}(-6))=c[/tex]
[tex]10=c[/tex]
Substitute the value of c in B
[tex]y=\frac{3}{2}x+10[/tex]
Hence the slope-intercept form of the equation of the line that passes through the point (–6, 1) and is perpendicular to the graph of 2x + 3y = –5? is [tex]y=\frac{3}{2}x+10[/tex]
When searching for a lost animal, the search party often creates a circular area with a search radius. Two points of interest in the search are the last known locations the animal was sighted. The two points of interest in this case are the pet’s home, which is located at (-4,5), and the neighbor’s yard, located at (-9,10). If the pet’s home is the center of the circle and the neighbor's yard is on the circle, find the radius of the circle.
The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?
what is the length of MN?
Searches related to Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.10, point, 1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe. Graph the shoe's altitude (in meters relative to the water's surface) as a function of time (in seconds).
Push technology is also known as _____.
simulcast
Webcasting
connectivity
data-driven decision-making
WEBCASTING
According to wikipedia ,
push technology is is a style of Internet-based communication where the request for a given transaction is initiated by the publisher or central server.
A webcast is a media presentation distributed over the Internet using streaming media technology to distribute a single content source to many simultaneous listeners/viewers.
martin paid $120 towards his $2400 credit card bill. what percentage did he pay
Find the percentages. 15m is what percent of 60m; 3m; 30m; 1.5 km?
Here are the calculations to find the percentages:
1. [tex]15\text{m}$ is what percent of $60\text{m}?[/tex]
[tex]\frac{15\text{m}}{60\text{m}} \times 100\% = \frac{1}{4} \times 100\% = 25\%[/tex]
2. [tex]15\text{m}$ is what percent of $3\text{m}?[/tex]
[tex]\frac{15\text{m}}{3\text{m}} \times 100\% = 5 \times 100\% = 500\%[/tex]
3. [tex]15\text{m}$ is what percent of $30\text{m}?[/tex]
[tex]\frac{15\text{m}}{30\text{m}} \times 100\% = \frac{1}{2} \times 100\% = 50\%[/tex]
4. [tex]15\text{m}$ is what percent of $1.5\text{km}?[/tex]
[tex]1.5\text{km} = 1500\text{m}[/tex]
[tex]\frac{15\text{m}}{1500\text{m}} \times 100\% = \frac{1}{100} \times 100\% = 1\%[/tex]
Therefore, the percentages are:
1. [tex]15\text{m}$ is $25\%$ of $60\text{m}[/tex]
2.[tex]15\text{m}$ is $500\%$ of $3\text{m}[/tex]
3. [tex]15\text{m}$ is $50\%$ of $30\text{m}[/tex]
4. [tex]15\text{m}$ is $1\%$ of $1.5\text{km}[/tex]
guy finds how car his house is several locations and makes the table shown how much farther away from guy's house is the library than the cafe?
what can you say about his average speed?
10 + 1 = a. dieciuno c. veintiuno b. once d. nueve
A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.
j is 25 more than 3 help
Leo multiplied all numbers from 1 to 11 and wrote the answer on the board. During the break three digits were erased 39,9...6,8... ... . What are the erased digits?
solve x=4+(4x-4)^(1/2)
Answer: Option B
x = 10
Step-by-step explanation:
just did it on edge
If the two equal sides of an isosceles triangle are 2 cm long, find the length of the third side thatmaximizes the area of the triangle.
what score must a student make on an algebra test to have an average score of 90 for the grading period. If his other test scores are 88, 84, and 92?
A pond is 50 m long 30 m wide and 2m deep find the capacity of the pond in cubic meters
how do you write 6 less than the product of 3 and a number X?
a sperical water tank holds 12,500 ft^3 of water what is the diameter of the tank
if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that the spherical water tank holds 12,500 ft³of water
We need to find the volume of the spherical water tank.
We know that volume of sphere=4/3πr³
Volume of sphere is 12,500 ft³
12500=4/3×3.14r³
12500=4.186r³
Divide both sides by 4.186
12500/4.186=r³
2986.144=r³
Take cube root on both sides
∛2986.144=r
14.40=r
We know diameter=2r
Diameter=2×14.4
=28.8=29
Hence, if a spherical water tank holds 12,500 ft³of water then the diameter of the tank is 29 ft.
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7 of every 20 employees at v&b bank company are between the ages of 20 and 30 if there are 13220 employees at B&B Bank company how many are between the ages of 20 and 30
Final answer:
To calculate the number of employees at V&B Bank Company between the ages of 20 and 30 out of the total 13,220 employees, we multiply 13,220 by the ratio of 7/20, yielding 4,627 employees in that age range.
Explanation:
The question asks how many employees at V&B Bank Company are between the ages of 20 and 30, given that 7 out of every 20 employees are in that age bracket and that the total number of employees is 13,220.
First, find the fraction of employees that are between the ages of 20 and 30 by dividing 7 by 20.
Fraction of employees aged 20-30 = 7 / 20
Next, calculate the number of employees in that age bracket by multiplying the total number of employees (13,220) by the fraction calculated above.
Number of employees aged 20-30 = 13,220 * (7 / 20)
By performing that multiplication:
Number of employees aged 20-30 = 13,220 * 0.35
Number of employees aged 20-30 = 4,627
Therefore, there are 4,627 employees at V&B Bank Company who are between the ages of 20 and 30.
What is the equation for 5n+7=21