Answer:
Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
What values of x and y satisfy the system of equations
{8x+9y=−3
{6x+7y=1
Answer:
• Let's first assign identifications to the equations given:
[tex]{ \rm{8x + 9y = {}^{ - }3 \: - - - \{equation \: (a) \} }} \\ { \rm{6x + 7y = 1 - - - \{equation \: (b) \}}} \\ [/tex]
• There are various methods to solve this system of equation, namely;
Graphical methodSubstitution methodElimination methodCalculus (Calculator synthetic method)1. Graphical method
→ You'll have to draw a graph, demacate it very well following the suitable scale.
→ Get values to plot from both equation (a) and equation (b).
→ Draw respective lines of each equation. The point of intersection of the lines is the answer of the values of x and y.
→ It'll be in coordinate format i.e; (x, y)
2. Substitution method
→ Lemme first consider equation (a)
[tex]{ \rm{8x + 9y = {}^{ - }3 }}[/tex]
• make x the subject of the equation (a):
[tex]{ \rm{8x = - 3 - 9y}} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8}y }} \: { \rm{- - - \{equation \: (c)}} \}[/tex]
→ Considering equation (b) next
[tex]{ \rm{6x + 7y = 1}}[/tex]
• substitute x in equation (b) with x in equation (c)
[tex]{ \rm{6( \frac{ - 3}{8} - \frac{9}{8}y ) + 7y = 1 }} \\ \\ { \rm{ - \frac{9}{4} - \frac{27}{4} y + 7y = 1}} \\ \\ { \rm{ \frac{1}{4} y = \frac{13}{4} }} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}[/tex]
• then find x using equation (c)
[tex]{ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y }} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8} (13)}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}[/tex]
3. Elimination method:
→ Here, we have to align the equations so that if we use addition or subtraction operations we remain with one term giving us zero [ eliminated ]
→ Multiply equation (a) by 6 and multiply equation (b) by 8. In order to eliminate x
→ Then we subtract equation (a) with equation (b)
[tex]{ \underline{ \rm{ - \binom{6(8x + 9y = - 3)}{8(6x + 7y = 1)} }}} \\ { \rm{ 0x \: - 2y = - 26 }} \\ \\ { \rm{ - 2y = - 26}} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}[/tex]
• find x using equation (c)
[tex]{ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}[/tex]
4. Calculator synthetic method:
→ To use this method, you must have a scientific calculator.
→ If you have it, follow the steps below;
Go to mode (press it 3 times until you see "EQN" )Press 1 or any number below the "EQN". It'll display "Unknowns" with 2 and 3 below it. 2 → Two equations system. 3 → 3 equations system.According to our question, it is a two equations system, press 2It'll display a, b and c [ a is the coefficient of x, b is the coefficient of y, c is the constant]For a1 press 8 then press "equal sign", b1 press 9, then equal sign, c1 press -3 then equal sign.Follow the same procedure for a2, b2 and c2Automatically, It will display the answersAnswer: x = -15, y = 13
Determine the range of the following graph:
Answer:
The range of x is -5 to +3
Step-by-step explanation:
Answer:
range means the value the x produces.
The range is -8 to zero.
Happy Learning
What is 3n^2 + 12n - 11 = 0
Answer:
n= plus or minus (+-) square root 69/ 3 -2
Step-by-step explanation:
Answer:
n = -2[+/-] (2 [tex]\sqrt{69}[/tex])/3
Step-by-step explanation:
in other words, the answer is
n=0.768875
and
n = -4.76887
What number is 12 more than 1/3 of itself?
Answer:
18
Step-by-step explanation:
Let the number be x.
1/3 of itself is 1/3 x or x/3.
x = x/3 + 12
3x/3 - x/3 = 12
2x/3 = 12
3/2 * 2x/3 = 3/2 * 12
x = 18
Answer: 18
The equation is formed as x - x/3 = 12. Then the solution of the equation will be 18.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number is 12 more than 1/3 of itself.
Let the number be 'x'. Then the equation is written as,
x = x/3 + 12
Simplify the equation, then the value of 'x' will be calculated as,
x - x/3 = 12
3x - x = 36
2x = 36
x = 36/2
x = 18
The equation is formed as x - x/3 = 12. Then the solution of the equation will be 18.
More about the solution of the equation link is given below.
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a remote control car costs $60. it is reduced to $45 in the sale. by what percentage was the price reduced
Answer:
25%
Step-by-step explanation:
Answer:
27%
Step-by-step explanation:
It was reduced by 27% because you get the 60 as 100% and 45 as 75% and you’ll get your answer.
How many you know that the expression is a perfect square trinomial pa help please
Multiply the roots of the first and third terms together. Compare to the middle terms with the result in step two. If the first and last terms are perfect squares, and the middle term's coefficient is twice the product of the square roots of the first and last terms, then the expression is a perfect square trinomial.
if I had made 450 cupcakes and sold 450 cupcakes for $0.85 how much money would I have made
Answer:
$382.5
Step-by-step explanation:
Find the value of x? LESSON Measuring Angles and Arcs Explain your reason
Answer:
50
Step-by-step explanation:
Sum of angles in a circle is 360,
145 + 165 + x = 360
310 + x = 360
x = 360 - 310
x = 50
Hi can someone answer this.
Answer:
hello again
Step-by-step explanation:
i think so,
hope it helped
for a poetry contest the minimum length of a poem is 16 lines. The maximum length is 32 lines. Write an absolute value equation that represents the minimum and maximum lengths
Answer:
lx-24l ≤ 8
Step-by-step explanation:
lx-24l ≤ 8
x ≤ 8 + 24
x ≤ 32
-----------------
-x + 24 ≤ 8
24 - 8 ≤ x
16 ≤ x
The absolute value equation that represents the minimum and maximum lengths is 8 = |x - 24|.
What is absolute value?Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.
For example, |5| is 5 because it is 5 units away from 0. Also, |-5| is also 5 because -5 is 5 units from 0.
We have been given that for a poetry contest the minimum length of a poem is 16 lines. The maximum length is 32 lines.
To determine the absolute value equation that represents the minimum and maximum lengths.
First, we need to find the difference between both solutions.
⇒ 32 - 16 = 16
Then, divide it by 2.
⇒ 16/2 = 8
⇒ 8 = |x - 32 + 8|
we could also write: 8 = |x - 32 + 8|
⇒ 8 = |x - 24|
Therefore, the absolute value equation that represents the minimum and maximum lengths is 8 = |x - 24|.
Learn more about the absolute value here:
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Two cyclists start from 98 miles apart and begin racing toward each other. Three hours later, they have not yet met and the distance between them is 2 miles. How fast is each of them biking if one bikes 3 mph slower than the other?
Answer:
18 and 21
Step-by-step explanation:
which pair of lines are parraell?
a.) x-5y = 10; y=5x-2
b.) x+y = 0; y=x+7
c.) 2x-3y=9; 4y =6x-20
d.) 4x-8y=8; y=2x+2
e.) 9x-3y=12; y=3x-10
Answer:
A.
Step-by-step explanation:
carry on learning.. and start reading your modules so u can learn <3
brainliest and follow please
What is an equivalent ratio of 5:9
Step-by-step explanation:
There is infinitely many ratios which are equivalent to 5:9. As we know always we can write divide as fraction, so . We can multiply nominator and denominator by the any number (but the same) and get another numbers but ratio will be the same, so equivalent.
For example
10:18,
15:27
Hope this helps.
Answer:
10:18
Step-by-step explanation:
Anything really just times both sides by the same number.
For example to get to 10:18 I multiplied both sides of 5:9 by 2.
If you were to multiply 5:9 by 3 (which would 15: 27) it would still be an equivalent to 5:9.
Find the area of a rectangular garden plot that measures 21 ft by 25.2 ft. Report with the correct number of significant digits.
The area of a shape is the amount of space it occupies.
The area of the garden is 529.2 square feet
The given parameters are:
Shape: Rectangle
Dimension: 21ft by 25.2ft
The area of a rectangle is:
[tex]\mathbf{Area = Length \times Width}[/tex]
So, we have:
[tex]\mathbf{Area = 21 \times 25.2}[/tex]
[tex]\mathbf{Area = 529.2}[/tex]
Hence, the area of the garden is 529.2 square feet
Read more about areas at:
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List the set of all even numbers between 2 and 10, inclusive.
Answer:
2, 4, 6, 8, 10
Step-by-step explanation:
If f(a) = 3a – a2, which of the following are not true statements?
Select all that apply.
f(4) = -4
f(3) = 0
f(-1) = 2
f(0) = 3
f(-5) = -40
3.68 divided by 0.001=?
Answer:
the answer is 3,680
Step-by-step explanation:
Hi!!!!! please anyone Can help this solve?
Answer:
The answer is 70%
Hope it helps <333
Step-by-step explanation:
A local maximum of the function f(x) occurs for which x-value?
Answer:
-4
Step-by-step explanation:
the highest f(x) value on the table is at -4 on the x column
All of the following are equivalent fractions except
8/40
3/15
6/30
5/20
Fill in all the missing measures. Show your work.
Answer:
B= 180-63
= 117°
E= 117°
Alternating angles are equal
Can someone please help
Answer:
63
Step-by-step explanation:
A median bisects the side that it is drawn to, so
DM = ME4x - 10 = 3x + 5x - 10 = 5x = 15So, FN = 4(15) + 3 = 63.
Once again, since a median bisects the side it is drawn to, NE = 63.
(ILL MARK BRAINLIEST)+ SHOW WORK PLS Jacob bought 12 chicken wings for $18. Fill out a table of equivalent ratios and plot
the points on the coordinate axes provided.
Five less than twice a number 581
Answer:
Step-by-step explanation:
Bro i dont know
I need help this please!
Answer:
I donot know
Step-by-step explanation:
l donot know you are question
Sarah has $30 and needs to buy some Halloween candy. Each bag of candy costs $5. the amount of money sarah has after purchasing x number of bags of candy can be represented by the function f(x)=30-5x. find the x intercept and the y intercept
Answer:
x means 10 sooooo
Step-by-step explanation:
hope it helps
100 POINTS ON THE LINE PLEASE HELP!!! ITS DUE TODAY AND I WILL GIVE BRAINLIEST. NO LINKS OR I WILL BE SAD
The graph for Airplane A shows the speed at which it travels as a function of time. The graph for Airplane B shows the distance it travels as a function of time.
Use the drop-down menus to complete the statements below about the two airplanes.
PART A: Describe the speed for each airplane from 0 to t1.
Airplane A travels at a speed that is (increasing, decreasing, 0, constant, but not 0).
Airplane B travels at a speed that is (increasing, decreasing, 0, constant, but not 0).
Part B: Describe the speed for each airplane from t1 to t2.
Airplane A travels at a speed that is (increasing, decreasing, 0, constant, but not 0).
Airplane B travels at a speed that is (increasing, decreasing, 0, constant, but not 0).
Answer:
from 0 to t1
Airplane A travels at a speed that is increasing.
Airplane B travels at a speed that is constant but not 0.
from t1 to t2
Airplane A travels at a speed that is constant, but not 0
Airplane B travels at a speed that is 0.
The airplane A is travelling at a faster and faster rate from 0 to t₁, and airplane B moves at a steady but not zero speed from 0 to t₁
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have a graph for Airplane A shows the speed at which it travels as a function of time. The graph for Airplane B shows the distance it travels as a function of time.
From the graph A and B
From 0 to [tex]\rm t_1[/tex]
Airplane A is travelling at a faster and faster rate.
Airplane B moves at a steady but not zero speed.
From [tex]\rm t_1[/tex] to [tex]\rm t_2[/tex]
Airplane A moves at a constant speed, but not at zero.
Airplane B is travelling at a speed of 0.
Thus, the airplane A is travelling at a faster and faster rate from 0 to t₁, and airplane B moves at a steady but not zero speed from 0 to t₁
Learn more about the line chart here:
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Factorise
x2 - 8x + 15
Answer:
[tex] {x}^{2} - 8x + 15 \\ (x - 5)(x - 3)[/tex]
I hope I helped you^_^
Answer:
(x-5) (x-3)
Step-by-step explanation:
At first find two numbers, that if you multiply, you get +15x², and the same number, if you do addition, get -8x
Those numbers are: -5x and -3x.
Now replace the -8x with the -5x and -3x. (x² - 5x - 3x + 15)
Now factorise as normal. You should get (x-5) and (x-3)
Hope I helped!
The graph shows the distance vs. time for a runner in a road race. Drag each number to the correct descriptor.
There are 268 lockers at Kortright Hills which are numbered from 1 to 268. All the locker doors are shut. On the first day of school, imagine that there are 268 students waiting out.
• The first student goes in and opens all the locker doors.
The second student goes in and closes every other locker door, starting with locker 2.
The third student goes in and changes every third locker, starting with locker 3 (If the do
open, it is closed. If the door is closed, it is opened.
The fourth students goes in and changes every fourth locker, starting with locker 4.
· This continues for all 268 students.
After all 268 students have entered the school, which locker doors will be open?
Answer:
289 student for the party them one mother say where you went that their mother where you want a brother se usse lion and the world I say diesel OK will die and back