Answer:
(3,2)
Step-by-step explanation:
Setting up equation so we can use substitution method
x - y = 1 , x + 3y = 9
step 1 set first equation equal to x by adding y to both sides so we can use the substitution method to solve the system of equations.
x = y + 1 , x + 3y = 9
now we can plug in ( or substitute hence substitution method ) the first equation into the second
Solving for y using the substitution method
x + 3y = 9
plug in x = y + 1
y + 1 + 3y = 9
combine like terms
4y + 1 = 9
subtract 1 from both sides
4y = 8
divide both sides by 4
y = 2
Now to find the value of x we plug in the value of y into one of the equations and solve for x.
Solving for x
x - y = 1
y = 2
x - 2 = 1
add 2 to both sides
x = 3
The solution would be (3,2)
Answer:
x = 3 and y = 2 or (3,2) in coordinate form
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]
Solve by elimination of x-terms by multiplying either one of equations with -1:
For this, I choose to multiply -1 in first equation:
[tex]\displaystyle \large{\begin{cases} -1(x-y=1) \\ x+3y=9 \end{cases}}\\\displaystyle \large{\begin{cases} -x+y=-1 \\ x+3y=9 \end{cases}}[/tex]
Then add both equations:
[tex]\displaystyle \large{-x+x+y+3y=-1+9}\\\displaystyle \large{4y=8}[/tex]
Divide both sides:
[tex]\displaystyle \large{\dfrac{4y}{4} = \dfrac{8}{4}}\\\displaystyle \large{y=2}[/tex]
Next, substitute y = 2 in one of equations to solve for x:
For this, I choose to substitute y = 2 in the first equation:
[tex]\displaystyle \large{x-y=1}[/tex]
Substitute y = 2 in:
[tex]\displaystyle \large{x-2=1}[/tex]
Add both sides by 2:
[tex]\displaystyle \large{x-2+2=1+2}\\\displaystyle \large{x=3}[/tex]
Hence, the solution is x = 3 and y = 2 or you can write as in coordinate form (3,2)
__________________________________________________________
First method is elimination method, I’ll demonstrate another method which is by using matrices to find the solutions.
Given:
[tex]\displaystyle \large{\begin{cases} x-y=1 \\ x+3y=9 \end{cases}}[/tex]
Write the system of equations in matrices form:
[tex]\displaystyle \large{\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]
Let:
[tex]\displaystyle \large{A=\left[\begin{array}{ccc}1&-1\\1&3\end{array}\right] }\\\displaystyle \large{X=\left[\begin{array}{ccc}x\\y\end{array}\right] \\\displaystyle \large{B = \left[\begin{array}{ccc}1\\9\end{array}\right] }[/tex]
From [tex]\displaystyle \large{AX=B \to X=A^{-1}B}[/tex] where:
[tex]\displaystyle \large{A^{-1}=\dfrac{1}{\det A} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] = \dfrac{1}{ad-bc} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right] }[/tex]
Find [tex]\displaystyle \large{\det A}[/tex]:
[tex]\displaystyle \large{\det A = ad-bc = 3+1=4}[/tex]
Therefore:
[tex]\displaystyle \large{A^{-1} = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right]}\\\therefore \displaystyle \large{X = \dfrac{1}{4}\left[\begin{array}{ccc}3&1\\-1&1\end{array}\right] \left[\begin{array}{ccc}1\\9\end{array}\right]}[/tex]
Evaluate the matrices:
[tex]\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3(1)+1(9)\\-1(1)+1(9)\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}3+9\\-1+9\end{array}\right] }\\\displaystyle \large{X= \dfrac{1}{4}\left[\begin{array}{ccc}12\\8\end{array}\right]}\\\displaystyle \large{X= \left[\begin{array}{ccc}3\\2\end{array}\right] }\\\therefore \displaystyle \large{\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}3\\2\end{array}\right]}[/tex]
Therefore, the solution is x = 3 and y = 2
For the diagram at right, write and solve an equation to find x
Answer:
x = 24
Step-by-step explanation:
The formula for determining the sum of interior angles is:
[tex](n-2) * 180[/tex]
[tex]4 * 180 = 720[/tex]
Therefore to determine an equation for x, we must add up all the interior angle equations and set them equal to 720.
[tex](2x+3) +(3x+12) + (7x+14) + (9x+2) + (4x+8) + (3x+9) = 720\\28x + 48 = 720\\28x = 672\\x = 24[/tex]
The equation and answer above shows how to find x, which equals 24.
What is the value of x^2+y^2 given the following system?
x+y=10
x-y=8
Answer:
I hope this helps, you can ask any questions for clarification
What scientific value for n will make this equation true? (4.8 × 10–3)(n) = 9.6 × 109 2.0 × 10–6 2.0 × 10–3 2.0 × 103 2.0 × 1012
The scientific value for n that will make the equation (4.8 × 10^(-3))(n) = 9.6 × 10^9 true is given by: Option D: 2.0 × 10^(12)
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
Scientific notations have some of the profits as:
Better readability due to compact representation
Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
Finding the value of n from the given equation:
[tex](4.5 \times 10^{-3}) \times n = 9.6 \times 10^9\\\\\text{Dividing both the sides by } (4.5 \times 10^{-3}) \\\\n = \dfrac{9.6 \times 10^9}{4.5 \times 10^{-3}} = \dfrac{9.6}{4.5} \times \dfrac{10^{9}}{10^{-3}}\\\\n \approx 2.1333 \times 10^{9-(-3)} = 2.1333 \times 10^{12} \approx 2.0 \times 10^{12}[/tex]
Thus, the scientific value for n that will make the equation (4.8 × 10–3)(n) = 9.6 × 10^9 true is given by: Option D: [tex]2.0 \times 10^{12}[/tex]
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Answer: D
Step-by-step explanation:
Paul is making grey paint. He mixes black and white paint in the ratio 1:3. He makes 35 litres of grey paint. How much white paint does he use?
What is the domain and range of the following graph
Answer:
Step-by-step explanation:
Domain is x-values the graph can have
x = [-3,22]
range is the y values the graph includes
range-= [-3,+2]
2. A traffic study was conducted on a busy street. In 15-minute intervals from 6:30 a.m. to 8:00
a.m., the number of vehicles that passed a certain point in one minute was recorded in the table
below. Write an equation for the curve of best fit, then approximate the number of cars that passed
the point at 9:15 a.m.
The line of best fit of the traffic study is a line through a scatterplot of data points which shows the relationship between the points.
How to illustrate the equation?Your information is incomplete as the table isn't given. Therefore, an overview will be given.
The least square methods is used by statisticians to arrive at the geometric equation for the line. A straight line will simply result from a simple regression of two or more independent variables.
A regression that has to do with multiple related variables lead to a curved line. The line of best fit is an important output of regression analysis.
A regression that has two independent variables will have a formula with:
y = c + b1x1 + b2x2
where,
c = constant
b1 = first regression coefficient
x1 = first independent variable
b2 = second regression coefficient
x2 = second independent variable.
In conclusion, the line of best fit expresses the relationship in a scatterplot of the data points.
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what is the constant of proportionality of the below
Answer:
Proportionality constant k
When two variables are directly or indirectly proportional to each other, then their relationship can be described as y = kx or y = k/x, where k determines how the two variables are related to one another. This k is known as the constant of proportionality.
Answer: Proportionality constant k
Step-by-step explanation:
below?
I need help on this one
X/3+7=12
Help :)
I need to write more to send it so…
Answer:
15
Step-by-step explanation:
To solve you have to get x by itself on one side.
x/3+7=12
First, you move the seven over.
x/3+7-7=12-7
Simplify.
x/3=5
Now to get x by itself you can multiply both sides by 3.
x/3*3=5*3
Simplify.
x=15
Answer:
x = 15
Step-by-step explanation:
x/3 + 3⋅7/3 = 12
x+3⋅7/3=12
x+21/3
X=15
A closet is in the shape of a rectangular prism. It is 214feet long, 3 feet wide, and 4 feet tall.
What is the volume of the closet?
7
f(x) = 3x2 + 4x – 7
g(x) = 2x – 11
Answer:
g[f(x)] = 6x² + 8x - 25
Step-by-step explanation:
g[f(x)] = g(3x² + 4x - 7)
= 2(3x² + 4x - 7) - 11
= 6x² + 8x - 14 - 11
= 6x² + 8x - 25
the volume inside a rectangular storage room is 2,025 cubic feet. the room is 9 feet high. find the the area of the floor.
Answer:
(Sorry if this answer is not correct, if it is or is not, please tell me in the comments!)
232.777778 feet squared (feel free to round the answer)
Step-by-step explanation:
The formula on how to find the volume is:
(the area of the floor) x (the height of the room) = 2025 cubic feet
We already know the height, so we need to plug it in.
(the area of the floor) x 9 feet = 2095 cubic feet
To get the area of the floor, we need to divide 2095 by 9.
So, the area of the floor is exactly 232.777778 feet squared.
Answer:
225 ft²
Step-by-step explanation:
Formula
Volume = Base Area x HeightVolume = 2,025 ft³Height = 9 ftSolving :
Base Area = Volume / HeightBase Area = 2,025 / 9Base Area = 225 ft²the phases in algebra are
Answer:
rhetorical stage, syncopated stage, symbolic stage
Step-by-step explanation:
28x+1=32x-1 solve for x
Answer:
x = 1/2
Step-by-step explanation:
28x + 1 = 32x - 1 <== subtract 28x from both sides
-28x -28x
1 = 4x - 1 <== add 1 to both sides
+ 1 + 1
2 = 4x <== divide both sides by 4 to isolate the variable
/4 /4
1/2 = x
Hope this helps!
[tex] \Large{\boxed{\sf x = \dfrac{1}{2} }} [/tex]
[tex] \\ [/tex]
Explanation:Given equation:
[tex] \sf 28x + 1 = 32x - 1 [/tex]
[tex] \\ [/tex]
Subtract 28x from each side :
[tex] \sf 28x + 1 - 28x = 32x - 1 - 28x \\ \\ \sf 1 = 4x - 1 [/tex]
[tex] \\ [/tex]
Add 1 to both sides:
[tex] \sf 1 + 1 = 4x \\ \\ \sf 2 = 4x [/tex]
[tex] \\ [/tex]
Divide both sides by 4:
[tex] \sf \dfrac{2}{4} = \dfrac{4x}{4} \\ \\ \\ \boxed{\boxed{\sf x = \dfrac{1}{2} }} [/tex]
[tex] \\ \\ [/tex]
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A pet store has 4 tanks of fish. Each tank has 32 fish. How many fish does the store have?
Answer:
128
Step-by-step explanation:
32 × 4 = 128
Each tank has 32, and there are four, so 32 times 4.
The store has 128 fish in the tank.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that pet store has 4 tanks of fish. Each tank has 32 fish.
Therefore,
Total fish = Number of fish that a tank can hold x Number of tanks
32 × 4 = 128
Hence, we get 32 for each tank, and there are four,
Thus, 32 times 4.
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How long does this lease last?
Is it possible to rewrite any proof that uses the AAS Congruence Theorem as a proof that uses the ASA Congruence Theorem? Explain your reasoning.
Answer: Yes
Step-by-step explanation:
If you were to use AAS, you could prove the third pair of angles congruent by using the fact that the sum of the measures of the angles of a triangle is 180 degrees, and since you have two of the angles, you can solve for the third pair of angles, which would be congruent.
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.15x2 − 6x + 400
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
The function of the production cost is a quadratic function, and the maximum production cost of the company is $340
How to determine the maximum production cost of the company?The function of the production cost is given as:
f(x) = 0.15x² - 6x + 400
Differentiate the function
f'(x) = 0.3x - 6
Set the function to 0
0.3x - 6 = 0
Add 6 to both sides
0.3x = 6
Divide both sides by 0.3
x = 20
Substitute x = 20 in f(x) = 0.15x² - 6x + 400
f(20) = 0.15 * 20² - 6 *20 + 400
Evaluate
f(20) = 340
Hence, the maximum production cost of the company is $340
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Please help The diagram below shows a square prism. The plane ABC is inside the
prism, and M is the midpoint of the base diagonal BC. MD. = square root 18
b Hence find, correct to the nearest degree, the angle that the plane ABC
makes with the base of the prism. Diagram is attached below.
Answer:
43°
Step-by-step explanation:
Triangle ADM is a right triangle with legs AD=4 cm and DM=√18 cm. The angle at M is the angle of interest. It can be found using the inverse tangent function.
Tan = Opposite/Adjacent
tan(∠AMD) = AD/MD = 4/√18
∠AMD = arctan(4/√18) ≈ 43.31°
The angle the plane makes is about 43°.
Answer:
the measure of the angle that the plane ABC makes with the base of the prism = 43 degree (to the nearest degree)
Step-by-step explanation:
We notice that the plane ABC and the base of the prism intersect along the line BC
And as the plane (ADM) is perpendicular to the line BC
then the angle between the plane ABC and the base of the prism is the angle AMD
Let θ be the measure of the angle AMD
[tex]\begin{aligned}\tan (\theta) &=\frac{A D}{M D} \\&=\frac{4}{\sqrt{18}}\end{aligned}[/tex]
[tex]\begin{aligned}\Rightarrow \theta &=\tan ^{-1}\left(\frac{4}{\sqrt{18}}\right) \\&=43,31385 \ldots\end{aligned}[/tex]
Jacob spent $34 on a magazine and seven notepads. if the magazine cost $6, then how much was each notepad?
Step-by-step explanation:
first you subtract 34 and 6 to get 28
now its 7 multiplyed by some number
each notepad 4 dollars cause 7x4=28
Answer:4 dollars
PLEASE HELP! PLEASE HELP! I NEED TO GET THIS RIGHT! PLEASE ANSWER FULLY!
Answer:
what do you need help with
y=4x+3 system of equations
Step-by-step explanation:
y=4x + 3
it should have another one
HELP PLEASE URGENT, ASAP. GRADE 11 TRIGONOMETRY MATH, ill give brainliest.
Answer:
deedww
Step-by-step explanation:
Which property of addition is shown below?
If x = a + bi and y = –a – bi, x + y = 0.
commutative property
identity property
associative property
inverse property
Answer: D
Step-by-step explanation:
Solve for x and y
7y - 5x = 45
x = 8 – 2y
Answer:
Hope the pictures will help you.
The solution to the system of equations is x = -2 and y = 5.
What is the solution to the system of equations?Given the parameters:
7y - 5x = 45
x = 8 - 2y
To solve the system of equations, substitute the expression for x from the second equation into the first equation.
7y - 5x = 45
Plug in x = 8 - 2y:
7y - 5( 8 - 2y) = 45
7y - 40 + 10y = 45
Collect and add like terms:
7y + 10y = 45 + 40
17y = 85
y = 85/17
y = 5
Plug the value of y into the second equation and solve for x:
x = 8 - 2y
Plug in y = 5:
x = 8 - 2( 5 )
x = 8 - 10
x = -2
Therefore, the value of x is -2 and y is 5.
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I got these three exercises that I gotta do and I need help. It’s in Hebrew but it would mean a lot if someone could help!
Answer:
i dont lnow the language sorry
Radius ob measures x units. which expression represents the circumference of the smaller circle with radius oa? (startfraction pi over 3 endfraction)x units (startfraction 2 pi over 3 endfraction)x units 2πx units 6πx units
The circumference of the smaller circle is C = 2*pi*x/3.
We have given that radius ob measures x units
What is the formula for the circumference of the circle ?circumference of the circle is given by,
[tex]C = 2\times \pi \times R[/tex]
where pi = 3.14
R= radius
we have two circles, A and B, where B is the larger circle and A is the smaller circle.
We know that,The circumference of B is 3 times the circumference of A.
The radius of circle B is OB = x
The radius of circle A is OA
We want to find an expression of OA.
The circumference of circle B is given by
[tex]C(B) = 2\times \piOB = 2\times pi\times x[/tex]
The circumference of circle A is given by
[tex]C(A) = 2\times\pi\times OA[/tex]
we know that the circumference of circle B is 3 times the circumference of circle A,
[tex]C(B) = 3\times C(A)[/tex]
replacing the equations for the circumferences
[tex]2\times\pi\times x = 3\times (2\times pi\times OA)[/tex]
We have divide both sides by [tex]2\pi[/tex]we get:
[tex]x = 3\times OA[/tex]
Now we want to solve this for OA, then we need to isolate it,
[tex]x/3 = OA[/tex]
We can conclude that the radius of the smaller circle is equal to x/3.
Then the circumference of circle A is
[tex]C(A) = 2\times pi\times x/3[/tex]
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Answer:
c
Step-by-step explanation:
Josh studied for his
science test from
3:45 p.m. until
5:30 p.m each day for
three days. how long
did he study in all?
he studied for 495 minutes. 165 minutes a day.
Answer: He studied for 315 minutes. Because he studied for 1hr and 45 mins (105 mins). Then you multiply this by 3 because it's been three days.
Hope this helps!
17=3x-4
Find the value of x
Answer:
x=7
Step-by-step explanation:
Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, ccc, Noah can use on each sandwich.
Answer:
24 / 6 = ccc
Step-by-step explanation:
There is 24 oz of cheese total that will be split evenly (divided) into 6 parts.
Each part will equal one sandwich worth of cheese (ccc) on the other side of the equation.
This one is very simple to solve, you could just calculate 24/6 to get your answer. But I'll go through it using typical algebra you would use for a less simple equation.
To solve:
Multiply by 6 to cancel the division by 6 on the left side
24 = 6ccc
Divide by 6 to isolate ccc again
4 = ccc
So each sandwich would get 4oz of cheese.