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
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use my gopuff code!! you can get $10 worth of free snacks!!! GOQYYW2X dont forget to use it at check out
A piece of wood measures 8.25 feet long. How long will each piece be if the wood is cut into 6 equal pieces ?
Answers
8.25/6 = 1.375
So each piece is 1.375 feet long
I hope this helps :)
What is the difference between the input and the output of a function
Answers
The input is the number you feed into equations, where as the output is the number you get when calculations are finished!
I hope this was helpful!!!
Alice makes a batch of cookies for her mom's
birthday. She adds 2 cups of flour and
1 cups of sugar to a bowl. How many cups of
dry ingredients does Alice add to the bowl?
Answers
Answer:
3 cups of dry ingredients.
Step-by-step explanation:
Sugar and flour are dry ingredients.
Answer:
3
Step-by-step explanation:
um 3? because 2 cups of flour + 1 cup of sugar = 3 cups of dry ingredients
21x
3
+28x
2
−49x−12x
2
−16x+28
Answers
Answer:
2
1
3
+
2
8
2
−
4
9
−
1
2
2
−
1
6
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8
Step-by-step explanation:
Let f(x)=x2+8x. Evaluate f(x)=--16
Answers
Answer:
-384
Step-by-step explanation:
f(x) =x^2+8x
evaluate f(x)=-16
input -16 for x
-16^2+8(-16)
-16^2= -256
then, 8*-16=-128
add the two negatives
-256+-128= -384
Round 733,400 to the nearest ten thousand
Answers
Answer:
730,000
Step-by-step explanation:
....
PLS HELP gIVING BRAINLIEST
Answers
Answer: i think it's b
Step-by-step explanation:
Because is get the same answer
Guided Practice
Identify the initial amount a and the growth factor b in the exponential function.
g(x) = 20 • 2x
A.
20; 2
B.
20; 2x
C.
40; 2
Answers
Answer:
A.
20; 2
Step-by-step explanation:
Your math problem
Help please help help please please please
Answers
Answer:
C. [tex] \frac{5}{4} [/tex]
D. [tex] \frac{6}{7} [/tex]
Step-by-step explanation:
C. [tex]2 - \frac{12}{16} [/tex]
[tex] = 2 - \frac{3}{4} [/tex]
[tex] = \frac{8 - 3}{4} [/tex]
[tex] = \frac{5}{4} [/tex]
D. [tex] \frac{20}{22} \times \frac{33}{35} [/tex]
[tex] = \frac{10}{11} \times \frac{33}{35} [/tex]
[tex] = 10 \times \frac{3}{35} [/tex]
[tex] = 2 \times \frac{3}{7} [/tex]
[tex] = \frac{6}{7} [/tex]
Which problem can be solved with the equation 1.75+(-1.75)=0?
Answers
Answer:
x+y=0
Step-by-step explanation:
x= 1.75
y= -1.75
x+y=0
Does the speedometer in a car measure velocity, speed, or both?
Answers
Answer:
the speedometer in a car only measures speed. hope this helps
Step-by-step explanation:
- Zombie
Answer: The speedometer on an automobile measures the vehicle's speed. The speed of a vehicle is measured in miles per hour or kilometers per hour by a speedometer. The velocity of a vehicle is not measured by a speedometer.
Maria's calculator showed the expression 23,000 + 4.5E3.What is another way to write the expression Maria's calculator showed?
Answers
Large numbers can be easily written to a required significant figures using the standard notation. So that, the expression on Maria's calculator also can be written in standard form as 2.75 x [tex]10^{4}[/tex]
An exponential function can be used when dealing with large numbers, which can also be written in a standard form. This helps to simplify and express large numbers scientifically.
The value on Maria's calculator = 23,000 + 4.5E3
But,
4.5E3 = 4.5 x 1000
= 4500
So that,
23,000 + 4.5E3 = 23,000 + 4500
= 27500
= 2.75 x [tex]10^{4}[/tex]
Thus,
23,000 + 4.5E3 = 2.75 x [tex]10^{4}[/tex]
Therefore, the expression on Maria's calculator also can be written in standard form as 2.75 x [tex]10^{4}[/tex]
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8. You need to make 120 servings of Caesar dressing. Each serving takes 2
teaspoons of crushed garlic. How many tablespoons of crushed garlic do you
need?
s out of 1.00
estion
Select one:
a. 120
X
b. 80
C. 240
d. 60
9. You need to make 54 servings of fried fish. Each serving takes 3 ounces of
nounds of four do you need?
Answers
240 teaspoons of crushed garlic is needed for 120 servings of Caesar dressing. While 162 ounces of flour is needed for 54 servings of fried fish
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Each serving takes 2 teaspoons of crushed garlic, hence for 120 servings:
number of teaspoons needed = 120 * 2 = 240
Each serving takes 3 ounces of flour, for 54 servings:
number of flour needed = 54 * 3 = 162 ounces
240 teaspoons of crushed garlic is needed for 120 servings of Caesar dressing. While 162 ounces of flour is needed for 54 servings of fried fish
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Coom
ements
The formula for the volume of a cylinder is V = xrh. The cylinder to the right has an exact volume of 720x cubic
meters. Find its height.
.6 m
The height of the cylinder is
(Simplify your answer.)
Answers
Answer:
You have the formula wrong.
The volume of a cylinder = PI * radius^2 * height
To find the height, the formula is:
height = volume / (PI*radius^2)
I'm assuming the radius = .6 meters so
height = 720 / (3.14159265 * .6^2)
height = 720 / 1.130973354
height = 636.61977 meters
Tp check your answer use this calculator: https://www.1728.org/diam.htm
Step-by-step explanation:
what is the difference between the highest and lowest temperature in the list below;
267°c,-78°c,19°c,38°c,-16°c
Answers
Use the number line to represent -4 1/2 plus 3 1/4
Answers
Start at - 4 1/2 adding a positive value moves to the right. Moving to the right 3 1/4 the slope becomes -1 1/4
Answer: -1 1/4
can someone answer
An artist used 666 tubes of red paint, 222 tubes of yellow paint, 131313 tubes of white paint, and 999 tubes of blue paint for a mural.
What is the ratio of tubes of red paint to tubes of white paint?
Answers
[tex] \huge \mathfrak{Solution : }[/tex]
Number of tubes of red paint = 666
Number of tubes of white paint = 131313
let's find their ratio :
[tex] \hookrightarrow \: \dfrac{666}{131313} [/tex][tex] \hookrightarrow \: \dfrac{222}{43771} [/tex][tex] \boxed{ \boxed{222 : 43771}}[/tex]Each lap around the track is 1/4 of a mile. How many laps will Quadir need to jog if he wants to jog 3 1/8 miles? Helpppp
Answers
9514 1404 393
Answer:
12 1/2 laps
Step-by-step explanation:
To find the number of laps, divide the distance by the distance per lap.
(3 1/8) ÷ (1/4) = (3 1/8) × (4/1) = 3·4 +(1/8)·4 = 12 4/8 = 12 1/2
Quadir needs to jog 12 1/2 laps if he wants to jog 3 1/8 miles.
Write an equation to model the sum of the situation below.
"A hydrogen atom has a zero charge because it has bne negatively charged
electron and one positively charged proton."
ASAPPPP
Answers
Answer:
1+-1=0 I would assume that would be sufficient unless Im underthinking it.
An equation to model the sum of the situation will be +1 - 1 = 0.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that "A hydrogen atom has a zero charge because it has been negatively charged electron and one positively charged proton."
The expression for the given situation will be written as below:-
+1 - 1 = 0
Therefore, the equation to model the sum of the situation will be +1 - 1 = 0.
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Solve the equation below
x/7 = 6
Answers
9514 1404 393
Answer:
x = 42
Step-by-step explanation:
You know from your multiplication tables that ...
42/7 = 6
x = 42
__
If you like, you can solve this by multiplying both sides of the equation by 7.
(x/7)(7) = 6(7)
x = 42
Answer: The correct answer is: " x = 42 . "
_____________________
Step-by-step explanation:
------------------------------------------
Given:
x/7 = 6 ; Solve for "x" ;
_____________________
"x" divided by "7" equals "6" ;
to solve for "x"
______________________
Multiply Each Side of the equation by "7" :
______________________
→ " 7 * [tex](\frac{x}{7}) = 6 * (7)[/tex] ;
______________________
On the "left-hand side" of the equation; the "7's" cancel out;
→ {since: " 7 / 7 = 1 " } ;
___________________
and on the "right-hand side" of the equestion:
→ 6 * 7 = 42 ;
___________________
So; we have: " x = 42 " ; which is our answer.
___________________
Hope this is helpful!
Best of luck to you!
___________________
If the risk-free rate is 10 percent and the market risk premium is 4 percent, what is the required return for the market?
Answers
Answer:
To calculate the market risk premium, simply subtract the risk-free rate from the market rate of return. For example, if the risk-free rate is 4 percent and the market rate of return is 10 percent, the market risk premium is 6 percent.
help right answer gets brainiest
Answers
D: Ray EA and ray EC
Can you guys please help with these questions I’m extremely stuck. It’s algebra 2 inverse functions.
Answers
9514 1404 393
Answer:
The graph of a function and its inverse are reflections of each other in the line y=xFor each ordered pair (x, y) in a function, the corresponding ordered pair in the inverse function is (y, x)see the attachment for the tables of valuesStep-by-step explanation:
Consider the function and its inverse shown in the second attachment. The function is ...
f = {(a, 3), (b, 1), (c, 2)}
The inverse function is ...
f^-1 = {(3, a), (1, b), (2, c)}
You will notice that the "x" and "y" of each pair are swapped between the function and its inverse. That is the point of an inverse function. It gives you the input that caused the function to create the output. For example, the pair (3, a) in the above inverse function tells you that the output 3 was the result of an input of 'a' to the original function.
__
On a graph, the swapping of input and output is essentially equivalent to relabeling the axes. If we keep the same x- and y-axis labels, it is equivalent to reflecting the function graph across the line y=x. That reflection is represented by the transformation (x, y) ⇒ (y, x).
__
The point of the exercise here is for you to identify some ordered pairs of one of the functions and realize that the inverse function reverses their order. You are to see that the graph of the function and its inverse are reflections of each other across the diagonal line y=x.
(- 3.5)(2/5)
A. -2 2/5
B. 1 2/5
C. -1 2/5
D. 2 2/5
Answers
Answer: C. -1 2/5
Step-by-step explanation:
Given expression
(-3.5) (2/5)
Convert decimal into fraction
=(-35/10) (2/5)
=[(-35 ÷ 5) / (10 ÷ 5)] (2/5)
=(-7/2) (2/5)
Simplify by multiplication
=(-7 × 2) / (2 × 5)
Cancel out 2 on both numerator and denominator
=-7/5
Convert improper fraction to mixed fraction
=[tex]\boxed{-1\frac{2}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The beginning mean bi-weekly wage in a certain industry is $1,891.00. If the mean bi-weekly wage grows by 5.75%, what is the new mean annual wage?
a
$42,056.00
b
$45,461.32
c
$49,166.00
d
$51,993.05
Answers
Answer:
51,993.05
Step-by-step explanation
Just took the test and got it right
What day is Memorial Day in 2021?
Answers
Answer:
Monday, may 31
have a good day
Geometry. Need help on how to solve G and H
Answers
Answer:
G) tan 60 = opp / adj = 30 / x
which equals
1.7321 = 30 / x
x = 30 / 1.7321
x = 17.3200161653
H) secant = hyp / adj
secant 30 = 16 / x
1.1547 = 16 / x
x = 16 / 1.1547
x = 13.8564
Here's a good site for trig functions : http://www.1728.org/trigcalc.htm
Step-by-step explanation:
what is the answer to 2/3 - 7/15=
Answers
Answer:
1/5
Step-by-step explanation:
2/3 - 7/15
Now when dealing with fractions, alas make the dominator ( bottom number the same), and the rule of thumb is, whatever u do to the bottom, must be done to the top
2 7
-------- - - - - - -
3 15
So now u should think, how to make 3 to 15, so u multiply it by 5, therefore u would also need to multiply it to the top
2 x 5 7
-------- - - - - - -
3 x 5 15
10 7
-------- - - - - - -
15 15
Now just minus horizontally ( u don't need to minus the dominator)
3
---------
15
Now can u make this fraction smaller? As in, is there a number that u can divide to the top and bottom, yes, that number is 3 in this case
3 ÷3
---------
15 ÷3
= 1
- - - - -
5
Thats your final answer
What common fraction (that is, a fraction reduced to its lowest terms) is equivalent to $.3\overline{25}$?
Answers
Answer:
it remains $3/$25
Step-by-step explanation:
[tex] \frac{3}{25} \\ [/tex]
