Answers
Answer:
x = 1y = -7Step-by-step explanation:
The coefficients of x and y do not have any "nice" relations, so doing this by elimination is just "brute force" with no particular subtlety.
After multiplying by appropriate numbers, you want the coefficient of one of the variables in one equation to be the opposite of the coefficient of the same variable in the other equation. Here, we can get that by multiplying the first equation by 7 and the second equation by 2.
7(2x +3y = -19) ⇒ 14x +21y = -133
2(-7x +2y = -21) ⇒ -14x +4y = -42
Adding these equations with opposite x-coefficients eliminates the x-terms. (That is how the "elimination" method gets its name.)
(14x +21y) +(-14x +4y) = (-133) +(-42)
25y = -175 . . . . . . . . simplify
y = -7 . . . . . . . . . . . divide by 25
Substituting this value into the first equation gives ...
2x +3(-7) = -19
2x = 2 . . . . . . . . . add 21
x = 1 . . . . . . . . . divide by 2
The solution is x = 1, y = -7.
_____
Additional comment
The multipliers used in this process are essentially the coefficients of one of the variables, with one of them negated. Here, we chose the x-coefficients, because negating one of them gives two positive multipliers. We judge it easier to do the arithmetic using positive numbers.
Had we chosen to use the y-coefficients (3 and 2) for our multipliers, we would probably multiply the first equation by 2, and the second equation by -3. That way, the remaining x-coefficient would be positive.
Planning ahead is helpful, but not essential. It can help to avoid errors and make the work easier to do.
Related Questions
more fr33 points for u amazing people, stream scientist by twice while ur at it!!!! :))
Answers
Answer:
ye
Step-by-step explanation:
Taylor Swift estimates the cost of a new Tesla model S to be $85,000. The actual cost is $100,690.
What is the percent error in Taylor's estimate? Round your answer to the nearest whole percent.
Answers
Answer:
should be 15%
Step-by-step explanation:
formula is |85,000 - 100,690| ÷ 100,690 × 100
The function f(x) goes through the point (4, 7). What point will this translate to in the function f(x) = (x - 6) + 3?
a. (10,10)
b. (-2,4)
c. (10,4)
d. (-2,10)
Answers
Answer:
a. (10,10)
Step-by-step explanation:
This was by accident the first answer is right
Please help asapppppp!!!!!
Answers
Answer:
x is 8.2 I think hold on
yeah I think
Functions f (solid) and g (dashed) are graphed.
What is the equation of g in terms of f?
A. G(x)=f(x)
B. g(x)=-f(x)
C. g(x)=f(-x)
D. g(x)=-f(-x)
Answers
3,080 feet = ____ miles. Answer as a proper fraction or as a whole or mixed number
Answers
Explanation:
There are 5280 feet in one mile so 3080/5280 is equal to 3080 ft/ 1 mile.
7/12 is equal to 3080/5280 when simplified.
4
to a improper fraction: 3 3/4 = 3 3/
4
= 3 · 4 + 3/
4
= 12 + 3/
4
= 15/
4
To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/
4
= 12/
4
b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.
Three and three quarters is fifteen quarters
Conversion a mixed number 2 2/
5
to a improper fraction: 2 2/5 = 2 2/
5
= 2 · 5 + 2/
5
= 10 + 2/
5
= 12/
5
To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/
5
= 10/
5
b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
c) Write a previous answer (new numerator 12) over the denominator 5.
Two and two fifths is twelve fifths
Multiple: 15/
4
* 12/
5
= 15 · 12/
4 · 5
= 180/
20
= 9 · 20/
1 · 20
= 9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the following intermediate step, cancel by a common factor of 20 gives 9/
1
.
In other words - fifteen quarters multiplied by twelve fifths = nine.
The rocket club is 60% boys. The number of boys is 3 less than 2 times the number of girls. Hov
many girls and how many boys are in the club?
Answers
Answer:
no of girls - 300
no of boys - 450
no of girls - 6
no of boys - 9
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
Given
Let boys be x and girls y
x = 2y-3
x - 2y = -3 ------(i)
x = 60/100(x+y)
10x = 6x + 6y
4x = 6y
2x = 3y
2x - 3y =0------(ii)
Subtract (ii) from (i)*2
no of girls - 6
no of boys - 9
to learn more about algebraic expression refer to:
https://brainly.com/question/4344214
#SPJ2
Find the exact value of the indicated trigonometric function of θ.
sin θ = [tex]\frac{1}{6}[/tex], sec θ < 0 Find cos θ and tan θ. ____________________
Answers
Answer:
cosθ = -√(35/36)
tanθ = -1/√35
Step-by-step explanation:
We know that
sin²θ + cos²θ = 1
(1/6)² + cos²θ = 1
1 - (1/6)² = cos²θ
35/36 = cos²θ
sec θ = 1/ cosθ
1/ secθ = cos θ
Because secθ < 0, 1/ secθ would also be < 0, so cos θ < 0
cosθ = -√(35/36)
tanθ = sinθ/cosθ = (1/6)/-√(35/36)
= (1/6) / -(√35/6)
= -1/√35
What is the domain and range?
Answers
Answer:
Domain: {-6, -2, -1, 1, 3, 6}
Range: {-6, -2, -1, 0, 3}
Step-by-step explanation:
to find the domain of a function, you look at all the possible x-values. this means you look at all the points, and see what their x-values are.
for example, the first point on the left is at (-6, -1). this means that -6 is in the domain. continue doing this for all the points, and you get {-6, -2, -1, 1, 3, 6}
to find the range of a function, it's just like domain but with y-values.
for example, for the leftmost point, it's at (-6, -1) so -1 is part of the range. continuing this with all the points, you get {-6, -2, -1, 0, 3}
A sports tournament has 6 teams. Each team has the same number of players. There are 60 players total. How many players does each team have?
Answers
Answer:
10
Step-by-step explanation:
because
60:6=10
every team has the same number of players
(it was an easy proble to solve thats why im typing , so i the app can confirm it as an answer)
bdbdbdndnfkkfkflfllflfkchchdhbdbenrnrnrnnrndndndndnddhjdjs
Answer:
10
Step-by-step explanation:
no. of teams=6
no. of players=60
no. of players in each team=60/6=10
Need help asap!! :) 2. Solve for x.
Answers
Ok done . Thank to me :>
0.326
In word form and stranded form please help!!?! I am taking things that are from 4th grade ahh I can't even remember anything from then. please help me word form and stranded form.
Answers
Answer:
three hundred twenty six thousandths
5x/2 - 3x/4 = 10 1/2
how to solve this?
Answers
[tex] \frac{5x}{2} - \frac{3x}{4} = 10 \frac{1}{2} \\ [/tex]
[tex] \frac{5x}{2} - \frac{3x}{4} = \frac{21}{2} \\ [/tex]
Multiply both sides by 4
[tex]4 \times ( \frac{5x}{2} - \frac{3x}{4} ) = 4 \times \frac{21}{2} \\ [/tex]
[tex]10x - 3x = 42[/tex]
[tex]7x = 42[/tex]
Divide both sides by 7
[tex] \frac{7x}{7} = \frac{42}{7} \\ [/tex]
[tex]x = 6[/tex]
if z=3+i/3-i find the value of 1/z and z+1/z
Answers
You are a civil engineer working on the design of a new
green space in your city. The space will include gardens,
playgrounds, and picnic areas. One section of the park will
be in the shape of a right triangle. A diagram of the
requirements for the triangular space is shown below.
2x+2 yards
2x yards
2x+4 yards
1. Explain what you know about the space you will be designing. List at least three pieces
of information. (2 points)
Answers
find three consecutive number whose sum shall equal 45
Answers
Answer:
14, 15, 16
Step-by-step explanation:
n + n+1 + n + 2 = 45
3n + 3 = 45
3n = 42
n = 14
14, 15, 16
What is the equation of the line that passes through the point (2,-2) and has a slope of -1/2?
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line
Answer:
y=-1/2x-1
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/2(x-2)
y+2=-1/2(x-2)
y=-1/2x+2/2-2
y=-1/2x+1-2
y=-1/2x-1
1) WET SURPRISE A water balloon is launched off of a patio. The path of the water
balloon can be modeled by h(t) = -6t2 + 13t + 5, where h(t) is the balloon's height in feet and t is the time in seconds after the balloon is launched.
a. How long will it take for the balloon to splat on the ground?
Answers
The function of the water balloon is an illustration of a quadratic function.
The balloon will splat on the ground after 2.5 seconds
The function is given as:
[tex]h(t) = -6t^2 + 13t + 5[/tex]
When the balloon splats on the ground, the value of h(t) is 0.
So, we have:
[tex]-6t^2 + 13t + 5 = 0[/tex]
Expand the expression
[tex]-6t^2 + 15t- 2t + 5 = 0[/tex]
Factorize the above expression
[tex]-3t(2t - 5)- 1(2t - 5 )= 0[/tex]
Factor out 2t - 5 in the 2t - 5
[tex](-3t - 1)(2t - 5 )= 0[/tex]
Split the equation into 2
[tex]-3t - 1 = 0\ or\ 2t - 5= 0[/tex]
Rewrite as:
[tex]-3t = 1\ or\ 2t = 5[/tex]
Solve for t
[tex]t = -\frac 13\ or\ t = \frac 52[/tex]
The value of t cannot be less than 0 i.e. negative.
So, we have
[tex]t = \frac 52[/tex]
Divide 5 by 2
[tex]t = 2.5[/tex]
Hence, the balloon will splat on the ground after 2.5 seconds
Read more about quadratic functions at:
https://brainly.com/question/11631534
express the radical using the imaginary unit i
Answers
Answer:
27
Step-by-step explanation:
At a salad bar, the cost per ounce is
$
0.85
, and the container costs
$
0.25
. Which function represents the total cost of a salad weighing
w
ounces, and what is the total cost,
C
, of a salad weighing
8
ounces?
Answers
Answer:
0.85 × 9.412=8.0002 nearest so 0.25 × 9.421= 2.35525
Step-by-step explanation:
A football team has a net yardage of −30 1 3 yards on a series of plays. The team needs a net yardage of 10 yards to get a first down. How many yards do they have to get on their next play to get a first down?
Answers
Answer:
36 yards
Step-by-step explanation:
10 yards needed minus 30 then add 1 and 3 and you have your answer
What is the result of 3 divided by three-fifths?
Answers
[tex]\dfrac{3}{\tfrac 35} = 3 \times \dfrac 53 = 5[/tex]
Answer:
5
Step-by-step explanation:
3 -> [tex]\frac{3}{1}[/tex]
Method is "Keep, Change, Flip"
[tex]\frac{3}{1} / \frac{3}{5} =\frac{3}{1} * \frac{5}{3} = \frac{15}{3} = 5[/tex]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
4(3q + 10) = 6( 2q - 9 )
Answers
Sorry if wrong
If the nominal interest rate is 4. 00% and the rate of inflation is 2. 25%, what is the real interest rate? 1. 75% 4. 50% 6. 25% 9. 0%.
Answers
Based on the information given the real interest rate is 1.75%.
Using this formula
Real interest rate =Nominal interest rate − Inflation rate
Where:
Nominal interest rate=4.00%
Inflation rate=2.25%
Let plug in the formula
Real interest rate=4.00%-2.25%
Real interest rate=1.75%
Inconclusion the real interest rate is 1.75%.
Learn more about real interest rate here:https://brainly.com/question/6106690
Find the magnitude of the following vector: v=15i + 8j
Answers
[tex]\text{Given that,}\\\\\vec{v} = 15 \hat{i} +8 \hat j\\\\ \\\text{Magnitude of the vector,}\\\\|\vec v| = \sqrt{15^2 +8^2}= \sqrt{289} = 17[/tex]
When you subtract a number, you get the same results as when you add the opposite number. Why?
Answers
Answer:
Step-by-step explanation:
Well, the opposite of a number is the same number with the opposite sign. For example, the opposite of -1 is 1.
So, say we have an equation where we're subtracting a number, for example, 2-1, which obviously equals 1. Now, if we add the opposite of 1 to 2, we get the equation 2+(-1) which still equals 1.
I hope this helps!
–A – 22 = –2A – 30
pls
Answers
Answer:
A= -8
Step-by-step explanation:
-A - 22=-2A-30
+2A +22
A = -8
15 POINTS! Will give brainliest to correct answer. I would love an explanation so I can do it on my own next time.
Answers
Answer:
Step-by-step explanation:
(A). A 90° counterclockwise rotation about the origin followed by a translation 1 unit to the left.
Answer my question 4 u could get 10 points
Answers
Answer:
30
Step-by-step explanation:
Split the trapezoid into parts, a rectangle and a triangle. The dimensions of the rectangle will be 3 and 8, so 3*8=24. 24 is part of the answer. The dimensions of the triangle are 4 and 3, and 4*3/2 is 6, so 6 is the other part of the answer. 24 + 6 = 30.
Multiply the fractions and reduce to lowest terms: 3/4 x 1/3
Answers
Answer:
3/12 or 1/4
Step-by-step explanation:
Answer:
1/4 is the answer.
Step-by-step explanation:
3/4 x 1/3
=> 3/12
=> 1/4
Therefore, 1/4 is the answer.
Hoped this helped.
