Answers
x is equal to 2 or -5
y is equal to 1 or 8
Step-by-step explanation:
first put your first equation in a format of y = x + _
here it will be :
[tex]y = - \times + 3[/tex]
now go and substitute this in your second equation. just like the picture. the pictures explain further
Hello there!
We are given the simultaneous equations:
[tex] \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]
There are many methods to solve the equation but the best way for this problem is Substitution Method.
First, we have to isolate one-degree variable. I will choose the first equation to isolate. We are going to isolate y-variable so we can substitute the first equation in the second.
[tex] \displaystyle \large{ \begin{cases} x + y = 3 \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]
Subtract x both sides for first equation.
[tex] \displaystyle \large{ \begin{cases} x - x+ y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]
After isolating y-term, we can finally substitute y = 3-x in the second equation.
[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} - 3(3 - x) = 1 \end{cases}}[/tex]
Expand -3 in. Recall that negative × negative = positive and negative × positive = negative.
[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 + 3x= 1 \end{cases}}[/tex]
Notice that the second equation is in quadratic pattern. We are going to convert in the standard form to solve the equation.
Subtract both sides by 1.
[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -10 + 3x= 0 \end{cases}}[/tex]
Arrange the expression in ax^2+bx+c = 0.
[tex] \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} -9 - 1 + 3x= 1 - 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y = 3 - x \\ {x}^{2} + 3x - 10= 0 \end{cases}}[/tex]
Factor the expression.
What two numbers add or subtract each others and equal to 3? (These numbers must not multiply each others and be greater than 10)
1+25-24-12+1What two numbers multiply each others and equal to -10?
Check the number above and multiply two numbers.
1×2 = 25×(-2) = -104×(-1) = -42×1 = 2Two numbers would be 5 and -2. Factor the expression in two brackets.
[tex] \displaystyle \large{(x + 5)(x - 2) = 0}[/tex]
Then we solve like a linear equation, isolate both x.
[tex] \displaystyle \large{x= - 5,2}[/tex]
We've got two x-values. But we are not done yet.
We are going to use these values to substitute in the simultaneous equation. You can substitute in any equations; the first or second. I will choose to substitute x = -5 or x = 2 in the first equation since it is faster.
[tex] \displaystyle \large{ \begin{cases} y= 3 - x \\ {x}^{2} - 3y = 1 \end{cases}}[/tex]
Substitute x = -5
[tex] \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 + 5\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 3 - ( - 5)\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 8\\ {x}^{2} - 3y = 1 \end{cases}} [/tex]
When we substitute x = -5, y = 8.
Next, substitute x = 2
[tex] \displaystyle \large{ \begin{cases} y= 3 -2\\ {x}^{2} - 3y = 1 \end{cases}} \\ \displaystyle \large{ \begin{cases} y= 1\\ {x}^{2} - 3y = 1 \end{cases}}[/tex]
When we substitute x = 2, y = 1.
Therefore,
x = -5, y = 8x = 2, y = 1OR
(-5,8) , (2,1) —> Coordinate Point formLet me know if you have any questions!
Topic: Simultaenous Equations
Related Questions
There are six teams in a high school bowling league. If each team will play against every other team two times, how many matches are scheduled?
Answers
Answer:
Step-by-step explanation:
What is the solution to this equation?
4(4x + 1) = 3x - 46 - x) + 8
Answers
Answer: Hello There!................
x=-3.5
Step-by-step explanation:
Mark me brainest please. Hope this helps. Anna ♥
Is the square root of 7 greater or less then 14/5
Answers
Answer:
less then
Step-by-step explanation:
the square root of 7 is 2.64 and 14/5 is = 2.8
The temperature is dropping 3 degrees every 4 hours.
It started at 62 degrees. What will the temperature be
in 16 hours? Please and Thank you !!
Answers
Answer: It will be 50º :)
Step-by-step explanation: 4 hours * 4 = 16, 3*4 = 12, 62- 12 = 50
Answer:
50 degrees
Step-by-step explanation:
16/4 = 4
4 * - 3 = - 12
62 - 12 = 50 degrees
Which of the following statements are true? Select all that apply.
Answers
Answer:
A,B,C
Step-by-step explanation:
the last number is the degree
Write in standard form.
y^2+14y-5x+64=0
Answers
[tex] \hookrightarrow \: {y}^{2} + 14y - 5x + 64 = 0[/tex]
[tex] \hookrightarrow \: 5x = {y }^{2} + 14y + 64[/tex]
[tex] \hookrightarrow \: 5x = {y}^{2} + 14y + 49 + 15[/tex]
[tex] \hookrightarrow \: 5x = (y + 7) {}^{2} + 15[/tex]
[tex] \hookrightarrow \: x = \dfrac{(y + 7) {}^{2} + 15 }{5} [/tex]
[tex] \hookrightarrow \: x = \dfrac{1}{5} (y + 7) {}^{2} + 3[/tex]
therefore, the correct option is B
Answer:
x = (1/5)(y + 7)² + 3
Step-by-step explanation:
Given that,
→ y² + 14y - 5x + 64 = 0
Let's find the required solution,
→ y² + 14y - 5x + 64 = 0
→ 5x = y² + 14y + 64
→ 5x = y² +14y +49 + 15
→ 5x = (y + 7)² + 15
→ x = [(y + 7)² + 15]/5
→ [x = (1/5)(y + 7)² + 3]
Hence, it is the correct answer.
please help me, if you help then thanks!
Answers
9514 1404 393
Answer:
27
Step-by-step explanation:
Evaluating this expression according to the order of operations is a straightforward calculator problem.
= (81 ÷ 27)³ = 3³ = 27
__
You can also use the rules of exponents to simplify this before evaluating.
(a^b)^c = a^(bc)
(a^b)/(a^c) = a^(b-c)
__
= ((3²)² ÷ 3³)³ = (3⁴ ÷ 3³)³ = (3¹)³ = 3³ = 27
The perimeter of an equilateral triangle is 3 (+ 5). The perimeter of a rectangle is 2 (2x - 3) + 2(2). If the perimeters of the two figures are equal, then what is the value of r?
Answers
Answer:
3.25
Step-by-step explanation:
Perimeter of triangle = 3(5) = 15 cm
Perimeter of rectangle = 2(2x - 3 + 4)
Perimeter = 2(2x + 1)
Perimeter = 4x + 2
4x + 2 = 15
4x = 15 - 2
4x = 13
x = 13/4
x = 3.25
Find the length of PQ if PQ = QR
Answers
Answer and Step-by-step explanation:
To find the length of PQ, we need to set the length of PQ equal to the length of QR (since in the question it tells us that PQ is equal to QR).
PQ = QR
x + 1 = 12
Solve for x.
Subtract 1 from both sides of the equation.
x + 1 - 1 = 12 - 1
x = 11
Now plug this number into the expression length for PQ.
11 + 1 = 12
The length of PQ is 12.
(you can also see that QR has a length of 12, so we can just say that PQ 12).
#teamtrees #PAW (Plant And Water)
I hope this helps!
Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a^(2x-1) equal to b ?
Answers
Answer:
x = 1/2
Step by step explanation:
Two numbers a and b are each greater than zero.
i.e a > 0 and b > 0
And;
[tex] \sqrt{a} \: = \: \sqrt[3]{b} [/tex]
Since the square root of a is equal to cube root of b then,
a = b = 1
[tex] {a}^{2x \: - \: 1} \: = \: b[/tex]
[tex] {1}^{2x \: - \: 1} = {1}^{0} [/tex]
2x - 1 = 0
x = 1/2
Two numbers are 'a' and 'b'.
And a > 0, b > 0
[tex]\sqrt{a}=\sqrt[3]{b}[/tex]
[tex]a^{\frac{1}{2} }=b^{\frac{1}{3}}[/tex]
[tex]a=(b)^{\frac{2}{3} }[/tex]
We have to find the value of [tex]x[/tex] if [tex]a^{2x-1}=b[/tex],
By substituting the value of [tex]a[/tex] in the given expression,
[tex](b^{\frac{2}{3}})^{2x-1}=b[/tex]
Now use the laws of exponents,
[tex]b^{\frac{2}{3}(2x-1)}=b[/tex] [Since, [tex](a^m)^n= a^{mn}[/tex]]
By comparing the exponents on both the sides,
[tex]\frac{2}{3}(2x-1)=1[/tex]
[tex]2(2x-1)=3[/tex]
[tex]4x-2=3[/tex]
[tex]4x=5[/tex]
[tex]x=\frac{5}{4}[/tex]
[tex]x=1.25[/tex]
Learn more,
https://brainly.com/question/219134
Write the equation of the line that passes through the points(-3,6) and (4,1). In point slope form
Answers
Answer:
y=10x-14
Step-by-step explanation:
From (4,1) on a graph, you would rise ten and then run to the left 14 times. Remember the rise/run and follow it. What I'm telling is rise you reach (4,6), then count across to (-3,6) to get your answer. You can use demos graphing calculator to help you better or make your own graph.
I hope this helped you! Comment below if you are confused or send a private message. ;)
What is the answer to
(9)(-2)=
Answers
Answer:
-18
Step-by-step explanation:
9 x -2 = -18
You multiply like normal and then for the answer just add a neg sign if there is an ODD amount of neg signs in the overall problem and then add no neg sigh if there are an EVEN number of neg signs (they cancel out),...
Hope it helps,... Chow,...!
Find the value of x and y. HELP ME PLSSS
Answers
9514 1404 393
Answer:
x = 17.3y = 28.6Step-by-step explanation:
The parallel lines divide each transversal proportionally.
x/30 = 15/26
x = 30(15/26) ≈ 17.3
__
y/16.5 = 26/15
y = 16.5(26/15) = 28.6
What is the coefficient of x?
Answers
Answer:
The coefficient of x is 1.
Step-by-step explanation:
If the question had asked for the coefficient of x^2 then it would be 3.
The coefficient of a variable is the number that is attached to it (the big number, not the exponent).
which value is equivalent to -5/6?
Answers
Answer:
-5/6 or -0.833333333333
Step-by-step explanation:
step-by-step-ecuation
Evaluate -7x + y5x
When x = -3, y = -9
Answers
Answer:
156
Step-by-step explanation:
-7(-3)+(-9)(5)(-3)
21+135
156
Answer:
156
Step-by-step explanation:
Substitute x and y values in the equation-7x+y5x
(-7)(-3)+(-9)*5*(-3)
21+135
156
Hope you got it
If you have any question just ask me
If you think this is the best answer please mark me as brainliest
Please help me in having a hard time
Answers
Answer:
10h^2
Step-by-step explanation:
i dont remember
Answer: 10h^2
Step-by-step explanation:
You’re gonna wanna combine your like terms, so…
([6h^2 + 8h^2] - 4h^2)
(14h^2 - 4h^2 = 10h^2)
So your answer would be: 10h^2
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
12 yd
6 yd
8 yd
16 yd
4 yd
Answers
help asap!!!!!!!!!!!!!!!
Answers
Answer:
Ray EA & Ray EC
(last one)
Step-by-step explanation:
Opposite rays make a 180 degree line.
For naming it, always start with the endpoint and then to the arrow.
Nine less than twice a number is the same as five times the number
Answers
Answer:
- 3
Step-by-step explanation:
2x - 9 = 5x
- 9 = 5x - 2x
-9 = 3x
-9/3 = x
x = -3
3.54 + 1.2 =
Explain how to get answer
Answers
how to plot 15/8 on a number line
Answers
1. Represent the fractions: 2/5, 11/5, -8/5 and -3/5 on a number line.
Since, the denominator of each given fraction is 5; divide the space between every pair of two consecutive integers (on the number line) in 5 equal parts. Each part so obtained will represent the fraction 1/5 and the number line obtained will be of the form:
Representing Fractions on Number Line
To mark 2/5; move two parts on the right-side of zero.
To mark 11/5; move eleven parts on the right-side of zero.
To mark -8/5; move eight parts on the left-side of zero.
To mark -3/5; move three parts on the left-side of zero.
Answer:
x : 15
y : 8
or
y : 15
x : 8
base of your graph
please helppp i’m so lost.
Some of the data in the table is numerical, while other data is categorical. Select all numerical data variables.
A. Calories
B.Manufacturer
C.Fat
D.Fiber
E.Sugar
F.Carbohydrates
G.Protein
H.Shelf
Answers
Answer:
Step-by-step explanation:
Protein ,fat and, calories. I think that’s it
Mr. Santiago can buy light fixtures in packages of 12 and light bulbs in packages of 9. He bought the fewest number of light fixtures and light bulbs so that there is exactly one bulb per fixture with none left over.
How many packages of light fixtures and how many packages of light bulbs did Mr. Santiago buy?
I WILL GIVE BRANLIEST PLEASE HELP AND RIGHT ANSWER
Answers
Answer:
3 and 4 packagesStep-by-step explanation:
We need to find the LCM of 12 and 9.
9 = 3*312 = 2*2*3Their LCM is:
LCM(12, 9) = 2*2*3*3 = 36Number of light fixtures and light bulbs is 36.
Number of packages will be:
36/12 = 3 and36/9 = 4 respectively.Step-by-step explanation:
First finding LCM of 9 and 12
9 = 3 × 3
12 = 2 × 2 × 3
LCM = 3 × 2 × 2 × 3
LCM = 36
Now,
No. of light fixtures = 36/12 = 3
No. of light bulb = 48/12 = 4
Determine the value of x
A. 13.95
B. 15
C. 4.375
D. 4.59
Answers
Answer:
A. 13.95
Step-by-step explanation:
By using the sine rule:
Rewrite in simplest terms: (4x + 6) – (3x + 1)
Answer:
Submit Answer
Answers
(4x + 6) - (3x + 1) = 4x + 6 - 3x - 1
= 4x - 3x + 6 - 1 = x + 5
Combine like terms:
x=7
PLS HELP ME GIVING BRAINLIEST AND POINTS
Answers
Answer:
-4(-4,2)
(16,-8)
option C is correct
Answer:
<16,-8>
Step-by-step explanation:
-4/9 ( 18/2 v)
First multiply
-4v
-4 < -4,2>
<16,-8>
Help me out please!!!!!
Answers
Answer:
A
Step-by-step explanation:
Isolate the variable by adding 1 to the whole comparison.
-7<x<6
Select the correct answer.
The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
A.
The mean of data set X is greater than the mean of data set Y.
B.
The median of data set X is less than the median of data set Y.
C.
The standard deviation of data set X is greater than the standard deviation of data set Y.
D.
The range of data set X is less than the range of data set Y.
E.
The mode of data set X is greater than the mode of data set Y.
Answers
Answer:
C. The standard deviation of data set X is greater than the standard deviation of data set Y.Step-by-step explanation:
A. The mean of data set X is greater than the mean of data set Y.
FALSE, there is no indication its true as per given statement.B. The median of data set X is less than the median of data set Y.
FALSE, there is no indication its true as per given statement.C. The standard deviation of data set X is greater than the standard deviation of data set Y.
TRUE, the greater the spread the greater the standard deviation.D. The range of data set X is less than the range of data set Y.
FALSE, the range of X would be greater with a greater spread.E. The mode of data set X is greater than the mode of data set Y
FALSE, there is no indication its true as per given statement.C.
C. The standard deviation of data set X is greater than the standard deviation of data set Y.
is a true statement .
Answer:
The spread of data set X is greater than the spread of data set Y, and the data sets are normally distributed. Which statement is true?
A.
The mean of data set X is greater than the mean of data set Y.False
B.
The median of data set X is less than the median of data set Y.False
C.
The standard deviation of data set X is greater than the standard deviation of data set Y.True
D.
The range of data set X is less than the range of data set Y.False
E.
The mode of data set X is greater than the mode of data set Y.False
Please Help me please hurry
Answers
Answer:
I think 3 $
Step-by-step explanation:
Ans; 9÷3=3 , 18÷6=3 ,....
I hope I helped you^_^
