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
Which of the following lines is perpendicular to the line with this equation ?
y =4/5X – 12
a. y= -4/5x +9
b. y=5/4x +4
c. y= -5/4x -15
d.y= 4/5x -5
Answer:
soln,
a
y=5/4×-15
Answer:
C: y = -5/4x - 15
Step-by-step explanation:
A perpendicular line is always the negative reciprocal of the slope. In this case, the slope is 4/5. Therefore, the negative reciprocal is -5/4. Only look at the numbers connected to X for the slope, do not look at the constant.
The flight of javelin released 6.5 feet from the ground at an initial velocity of 68 feet per second is modeled by the function h=-16^2+6.5 where h is the height of the javelin in feet after r seconds . Determine how many seconds it will take the javelin to reach the maximum height and find the maximum height. Round to the nearest hundredth if necessary
Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the height is modeled by:
h(t) = -16t² + 68t + 6.5.
The coefficients are a = -16, b = 68, c = 6.5, and the vertex will be given by:
[tex]x_v = -\frac{b}{2a} = -\frac{68}{-32} = 2.13[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{68^2 - 4(-16)(6.5)}{-64} = 78.75[/tex]
A maximum height of 78.75 feet is reached after 2.13 seconds.
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
can someone help me.
Step-by-step explanation:
side of square = 10
area of square = side² = 10² = 100 cm²
P.S : ARE YOU SURE THE OPTIONS ARE CORRECT ???
What is the surface area? 34 in 30 in 34 in 32 in 36 in
Answer:
If I am correct to work out the surface area you need to do base times height so the calculation would be...
32(base) × 30(height)
which equals 960 square inches
Please do check with someone else the answer, as I am not that confident and new
determine how many ways a president, vice president and treasurer can be chosen from a math club that has 7 members.
Answer:
210
Step-by-step explanation:
There are 7 choices for president.
Then there are 6 choices for vice-president.
Finally, there are 5 choices for treasurer.
7 × 6 × 5 = 210
Help me with this assignment please I don’t understand it
Complete the reasons for the proof.
given:
m 3 = m 4
Prove 1 and 2 are supplementary
Answer:
m3 and m4 are supplementary
Step-by-step explanation:
since m3 and m4 are supplementary, we can state that m3 and m4 are supplementary
see full explanation in the vid below
Suppose that a classmate asked you why (2x + 112 is not (4x² + 1). What is your response to this classmate?
O A. An expression such as (2x + 1)2 is called the square of a monornial. The expression (2x + 1)2 is equal to (22• 2xX1. 1), thus it is not equivalent to
(4x2 +1)
B. The classmate is correct. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2)?(x} = (132, thus it is
equivalent to (4x + 1)
OC. An expression such as (2x + 1)2 is called the square of a binomial. The expression (2x + 1)2 is equal to (2x+ 1x2x + 1), thus it is not equivalent to
(4x + 1)
OD. An expression such as (2x + 1)2 is called the product of the sum and difference of two terms. The expression (2x + 1)2 is equal to (2x+ 1(2x - 1), thus it is
not equivalent to (4x2 + 1)
+
The given expression is the square of a binomial, such that:
(2x + 1)^2 = 4x^2 + 4x + 1
Then the correct option is C.
Are the expressions equivalent?We want to see if:
(2x + 1)^2
Is equivalent to (4x^2 + 1).
First, this is false, let's prove that.
We have the square of a binomial (2x + 1)^2. Remember the general formula:
(a + b)^2 = a^2 + 2ab + b^2
So if we apply this to our expression we get:
(2x + 1)^2 = (2x)^2 + 2*2x*1 + 1^2 = 4x^2 + 4x + 1
Then, the correct option is C.
If you want to learn more about binomials, you can read:
https://brainly.com/question/15246027
Please help with this problem.
Answer:
whats the problem it doesnt say anything
what expression is equivalent to 1/4 (x+24)
Use the Distributive Property, which states the following:-
[tex]\sf{a(b+c)=ab+ac}[/tex]
Where
we distribute a by multiplying it times b and c
a, b, and c can be either constants (numbers) or variables (letters)
Distribute:-
[tex]\sf{\displaystyle\frac{1}{4}(x+24)}}[/tex]
Multiply the term before the parentheses by the terms inside the parentheses:-
[tex]\sf{\displaystyle\frac{1}{4} x+6}}[/tex]
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
C is a circle with centre (0,0)
L is a straight line with negative gradient.
The circle C and the line L intersect at the points A and B.
The coordinates of A are (-9,2)
The x coordinate of B is 7
Find an equation of L.
Answer:
Step-by-step explanation:
Factor x^2−2x. Is this a special product?
Answer:
x(x-2)
Step-by-step explanation:
x^2−2x
Factor out an x
x(x-2)
This is not a special product
[30 PTS!!] Using mathematically precise language, explain in detail how you would multiply the complex number [tex]z_1=r_1(cos[/tex]θ[tex]_1+i sin[/tex]θ[tex]_1)[/tex] with the complex number [tex]z_2=r_2(cos[/tex]θ[tex]_2+isin[/tex]θ[tex]_2)[/tex].
Multiplying z₁ and z₂ involves calculating their products
The product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
How to multiply the complex numbers?The numbers are given as:
z₁ = r₁(cosΘ₁ + isinΘ₁)
z₂ = r₂(cosΘ₂ + isinΘ₂)
The product is represented as:
z₁ * z₂ = r₁(cosΘ₁ + isinΘ₁) * r₂(cosΘ₂ + isinΘ₂)
This gives
z₁ * z₂ = r₁r₂(cosΘ₁ + isinΘ₁) (cosΘ₂ + isinΘ₂)
Expand
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ + i²sinΘ₁sinΘ₂ )
In complex numbers,
i² = -1.
So, we have:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ - sinΘ₁sinΘ₂ )
Rewrite as:
z₁ * z₂ = r₁r₂(cosΘ₁cosΘ₂ - sinΘ₁sinΘ₂ + icosΘ₁sinΘ₂+ isinΘ₁cosΘ₂ )
Apply sine and cosine ratios
z₁ * z₂ = r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Hence, the product of z₁ and z₂ is r₁r₂(cos(Θ₁ + Θ₂) + isin(Θ₁ + Θ₂))
Read more about complex numbers at:
https://brainly.com/question/10662770
Work out the size of angle x.
Answer:
47
Step-by-step explanation:
because you know that a triangle is 180 degrees and you have the other two degrees, so all you have to do is add 90 (the little box in the corner means 90) +43=133 and subtract by 180 giving you 47 as your answer.
Answer:
Heya! ^^
let's first look at some terms that may help us understand the concept of the question better.
______________________________________
★ Angle sum property of triangle states that the sum of all the angles of a triangle equals 180°
______________________________________
now let's come over what the question says.
we've been given a right angled triangle with measure of one of its angle as 43°.
we've to calculate the measure of the third angle named " x "
therefore ,
[tex]by \: angle \: sum \: property \: of \: triangle \\ \\ 90\degree + 43\degree + x = 180\degree \\ \\ 133\degree + x = 180\degree \\ \\ x = 180\degree - 133\degree \\ \\ x = 47\degree[/tex]
thus the measure of x is 47°.
hope helpful :D
Jack has $1,331 in an account that earns 5% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Answer:
$1540.80
Step-by-step explanation:
Answer: 1540.80
Step-by-step explanation: i got it right on my ixl
Which expressions are polynomials?
Select each correct answer.
Answer:
b and d option are correct
Answer:
B, D
Step-by-step explanation:
B, D
x cannot be in a root. (A)
x cannot be in the denominator. (C)
Please help I will give brainliest.
Answer:
The weight, in pounds, of one bag of beans.
Step-by-step explanation:
Since we know that there are 15 bags of beans, we can eliminate the first option and anything about something other than th e beans. Also, we know that we are not given the information on how heavy the bag of beans are, so with process of elimination, the 3rd one is the answer.
I hope this helped!
It would be greatly appreciated if you marked this answer as brainliest!
If u = ❬6, –9❭ and v = ❬–24, 36❭ with an angle θ between the vectors, are u and v parallel or orthogonal? Explain.
The vectors are parallel because cos θ = −1.
The vectors are parallel because u • v = 0.
The vectors are orthogonal because u • v = 0.
The vectors are orthogonal because cos θ = −1.
The vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
How to determine the relationship between two vectors
By linear algebra we can use the definition of dot product to determine the relationship between two vectors, whose cases are described below:
Two vectors are orthogonal if and only if cos θ = 0.Two vectors are parallel if and only if cos θ = 1 or cos θ = -1.And the expression for the cosine of the angle between the two vectors is:
[tex]\cos \theta = \frac{\vec u \,\bullet\,\vec v}{\|\vec u\|\cdot \|\vec v\|}[/tex] (1)
Where [tex]\|\vec u\|[/tex] and [tex]\|\vec v\|[/tex] are the norms of the two vectors, which are determined by Pythagorean theorem.
Now we proceed to calculate the angle between the two vectors:
[tex]\cos \theta = \frac{(6)\cdot (-24)+(-9)\cdot (36)}{(3\sqrt{13})\cdot (12\sqrt{13})}[/tex]
cos θ = -1
Thus, the vectors u = ❬6, –9❭ and v = ❬–24, 36❭ are parallel to each other because the cosine of the angle θ is equal to -1. (Right choice: A)
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477
The radius of a circle is 16 cm. Find its area in terms of pi
jason is wrapping a gift.The box he is using is a rectangular prism with a length of 20 inches a width 12 inches and a height of 5 inches.Find how many square inches of paper does he need to wrap the intire box?
Answer:
Step-by-step explanation:
Surface area of rectangular prism:
length = l = 20 in
width = w = 12 in
height = h = 5 in
[tex]\boxed{\text{surface area of rectangular prism = 2*[lw + wh + hl]}}[/tex]
= 2* [ 20*12 + 12*5 + 5*20]
= 2* [240 + 60 + 100]
= 2 * 400
= 800 in²
Val is going to plant b vegetable seeds in one garden and 3b + 10 vegetable seeds in another. How
many seeds is Val going to plant?
Val is going to plant seeds.
Answer:
The question is not showing what we are supposed to find.
b+3b+10
help , i need to finish this today :)
Use the equation of the curve of best fit to predict what the daily rental price for a two-bedroom condo will be in June and in January.
Type the correct answer in each box.
The daily rental price will be $ _____in June and $ _____ in January.
Hii!
let me answer this for you before i head out!
So, how many days are in 1 week? 7.
To rent daily, we need to find out the price for 1 single month.
1 month is $154
7 times what is 154?
7x22 is 154
Therefore, to rent a room everyday, it would cost 22$ for the first month.
437 divided by 2 is 218
218 divided by 7 is 31
Hope it helps
Sorry if its wrong!
rearrange q=w/3-7 to make w the subject
q=w/ 3-7
q(3-7)= w
hope this helps :)
Answer:
w = 3q + 21
Step-by-step explanation:
assuming you mean
q = [tex]\frac{w}{3}[/tex] - 7 ( add 7 to both sides )
q + 7 = [tex]\frac{w}{3}[/tex] ( multiply both sides by 3 to clear the fraction )
3(q + 7) = w , that is
w = 3q + 21
An airplane flies with a constant speed
of 640 km/h. How long will it take to
travel a distance of 640 kilometers?
The time it would take to travel a distance of 640 kilometers is 1 hour
Speed, distance and timeFrom the question, we are to determine how long it would take the airplane to travel a distance of 640 kilometers.
From the give information,
The airplane flies with a constant speed of 640 km/h.
Speed = 640 km/h
Distance to be covered = 640 km
From the formula,
[tex]Speed = \frac{Distance}{Time}[/tex]
We can write that
[tex]Time= \frac{Distance}{Speed}[/tex]
∴ [tex]Time = \frac{640 \ km}{640 \ km/h}[/tex]
Time = 1 hour
Hence, the time it would take to travel a distance of 640 kilometers is 1 hour
Lear more on Speed, distance and time here: https://brainly.com/question/17146782
4/15, 5/27, 7/18 Arrange the fractions in ascending order
Answer:
Take lcm and see
Step-by-step explanation:
5/27 ;4/15 ;7/18
B
An athlete ran uphill at 3 metres per second for x seconds , downhill
at 6 metres per second for y seconds and covered a total distance
of 375 metres . If the athlete took 5 seconds longer to run uphill than
downhill, calculate the values of xandy.
(5)
Step-by-step explanation:
- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.
- Only the speed of going up the hill and down the hill will be different.
In the figure shown, what is the measure of angle x?
Triangle ABC has measure of angle BAC equal to 40 degrees and the measure of angle ABC is equal to 70 degrees. The side BC of the triangle is extended till D. The angle ACD is labeled as x.
100 degrees
110 degrees
120 degrees
140 degrees
➾Firstly, we will find the measure of [tex]\angle[/tex]ACB.
We know that,
Sum of all interior angles of a triangle = 180°.
[tex]\rightarrow[/tex][tex]\angle[/tex]BAC + [tex]\angle[/tex]ABC + [tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] 40°+70°+[tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] 110°+[tex]\angle[/tex]ACB = 180°
[tex]\rightarrow[/tex] [tex]\angle[/tex]ACB = 180°-110°
[tex]\rightarrow[/tex][tex]\angle[/tex]ACB = 70°
So, the measure of [tex]\angle[/tex]ACB = 70°.
➾ Side BC of the triangle is extended till D. So, we have to find the measure of [tex]\angle[/tex] ACD.
As we know that,
Sum of any two or more angles that lie on a straight line = 180°.
So, [tex]\sf\angle{ACB}[/tex]+[tex]\sf\angle{ACD}[/tex] = 180°
[tex]\rightarrow[/tex] 70° + [tex]\sf\angle{ACD}[/tex] = 180°
[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 180°-70°
[tex]\rightarrow[/tex][tex]\sf\angle{ACD}[/tex] = 110°.
Therefore, measure of [tex]\sf\angle{ACD}[/tex] = 110°.
____________________________
Hope it helps you:)
help :(
“two less than a number is less than or equal to thirty three”
- The inequality translated in numerical form
- The solution in set notation
- The solution in interval notation
Answer:
- The inequality translated in numerical form
Step-by-step explanation:
2.56x+0.14-187x
How to solve pls and answer
3 A packet contains 1.5 kg of oats.
oats
OO
1.5kg
Every day Maria uses 50 g of oats to make porridge.
How many days does the packet of oats last?
Answer:
30 days
Step-by-step explanation:
1.5 Kg = 1500 g
Using 50 g a day
Number of days
= 1500 / 50
= 30 days.
