Solve the following system of equations graphically on the set of axes below.
y=x+1
3x+y=−7
(worth 60 points)
Answers
Answer:
(-2, -1)Step-by-step explanation:
Given system:
y = x + 13x + y = − 7Graph each line and find the point of intersection of lines.
Graphical solution is attached.
The solution is (-2, -1)
(-2, -1)
y = x + 1 ... (1)
3x + y = -7 ... (2)
Graph in the picture.
Related Questions
A particle moves along the x-axis so that time t>0 the position is given by x(t)=0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1. What is the velocity of the particle at the first instance the particle is at the origin?
Answers
The velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
To find the velocity of the particle at the first instance it is at the origin, we need to find the value of t when x(t) = 0.
Since the particle is at the origin when x(t) = 0, we have:
[tex]0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1 = 0[/tex]
Using numerical methods or graphing the equation, we find that the roots are approximately t ≈ -0.618, t ≈ 1.532, t ≈ 3.143, and t ≈ 2.944.
Since t > 0, the first instance the particle is at the origin corresponds to t ≈ 2.944 (the smallest positive real root).
Now, to find the velocity of the particle at this instance, we need to find the derivative of the position function x(t) with respect to time t, which gives us the velocity function v(t):
v(t) = dx/dt
[tex]v(t) = d/dt (0.5t^4 - 1.5t^3 - 2t^2 + 6t - 1)\\v(t) = 2t^3 - 4.5t^2 - 4t + 6[/tex]
Now, we can find the velocity at t ≈ 2.944:
[tex]v(t = 2.944) = 2(2.944)^3 - 4.5(2.944)^2 - 4(2.944) + 6[/tex]
v(t ≈ 2.944) ≈ 16.885
So, the velocity of the particle at the first instance it is at the origin (approximately t ≈ 2.944) is approximately 16.885 units per time unit.
learn more on velocity :
https://brainly.com/question/29290259
#SPJ4
are 16/72 and 18/81 equivalent rational numbers
Answers
Answer:
yes
Step-by-step explanation:
[tex]\frac{16}{72}[/tex] ( divide numerator/ denominator by 8, the LCM of 16 and 72 )
= [tex]\frac{2}{9}[/tex]
[tex]\frac{18}{81}[/tex] (divide numerator/ denominator by 9 the LCM of 18 and 81 )
= [tex]\frac{2}{9}[/tex]
Both rational numbers simplify to [tex]\frac{2}{9}[/tex] and are equivalent
If K = F( A + B ) , find “ A ” if F = 2 , B = 3 , K = 10
Answers
Answer:
The value of A is 2
Step-by-step explanation:
F = 2 , B = 3 , K = 10
K = F( A + B )
10 = 2(A + 3)
10 = 2A + 6
Now, Subtract 6 from each side we get,
10 - 6 = 2A + 6 - 6
4 = 2A
2A = 4
Now, divide both side by 2 we get,
2A/2 = 4/2
A = 2
Thus, The value of A is 2
FOR VERIFICATION ONLY :-K = F( A + B )
10 = 2(2 + 3)
10 = 2(5)
10 = 10
L.H.S = R.H.S
Hence Proved!
-TheUnknownScientist 72
help - does anyone know how to calculate the gradient of this?
Answers
Answer:
To calculate the gradient of a straight line we choose two points on the line itself. From these two points we calculate: The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates). If the answer is a positive value then the line is uphill in direction.
If the answer is positive value then the line is uphill in direction
If the answer is negative value then the line is downhill in direction
Simplify (12+3i)−(−5+2i)
Answers
Answer:
17+5i
Step-by-step explanation:
add the like terms
double negative equals positive
;)
Answer:
17+i
Step-by-step explanation:
Answer ASAP please<3
Answers
Step-by-step explanation:
So if you multiply both the numerator and denominator by the same number, you get the initial number. Your goal here is to get the same denominator so that you can solve the problem easily! hope it helped!
solutions: ( x = 2 & x = -2 )
Answers
hmmmmhmmmmmmmmmmmmmmmmmmmmmm
What is the diameter of a circular swimming pool with the radius of 8 feet
Answers
What is the slope of this graph?
A-4
B 1/4
C-1/4
D 4
Answers
Answer:
The answer is D
Step-by-step explanation:
The line has 2 points: (-1;0) and (0;-4)
=> x1 = -1; x2 = 0 => x1 - x2 = -1 - 0 = -1
y1 = 0; y2 = -4 => y1 - y2 = 0 - 4 = -4
=> slope = (y1 - y2)/(x1 - x2) = [tex]\frac{-4}{-1}[/tex] = 4 => D
A necklace is made from 2 purple pyramids and 12 yellow spheres. What is the ratio of pyramids to spheres in its simplest form?
Answers
Answer:
1:6
Step-by-step explanation:
2:12
\/
1:6
Have a nice day!
If this is not what you are looking for - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
1:6
Step-by-step explanation:
2/12 = 1/6
PLZ HELP!!!!
Use the function f(x)=x^2+4x-5 and the coordinate plane. SHOW ALL WORK FOR EACH PART!
What are the values of a, b, and c? (3pts)
Does the parabola open up or down? How do you know? (2pts)
What is the maximum or minimum value? How do you know? (2pts)
What are the x-intercepts? (2pts)
What is the y-intercept? (1pt)
What is the vertex? (2pt)
Answers
9514 1404 393
Answer:
a) a=1, b=4, c=-5
b) opens up; a > 0
c) minimum = -9, the y-value of the vertex
d) x = -5, 1
e) y = -5, the value of c
f) (-2, -9)
Step-by-step explanation:
A graph drawn by a graphing calculator can answer all of these questions quickly and easily.
__
a) The values of 'a', 'b', and 'c' are the values of the coefficients of the terms in the function definition. They refer to the coefficients in the standard form:
f(x) = ax^2 +bx +c
f(x) = x^2 +4x -5 . . . . . . . your equation with a=1, b=4, c=-5
__
b) The parabola opens up. This is because the value of 'a' is greater than zero.
__
c) The minimum is the y-value of the vertex. When the function is written in vertex form it is ...
f(x) = (x -h)^2 +k . . . . . . . . . . . vertex (h, k)
Your function can be put into this form:
f(x) = x^2 + 4x +4 -5 -4 . . . . . . add and subtract 4 to complete the square
f(x) = (x +2)^2 -9 . . . . . . . . vertex form. The vertex is (-2, -9).
The y-value of the vertex is -9, the minimum value of the function.
__
d) Solving f(x) = 0, you get ...
(x +2)^2 -9 = 0
(x +2)^2 = 9 . . . . . . . . add 9
x +2 = ±√9 = ±3 . . . . . take the square root; next, subtract 2
x = -2 ±3 = {-5, 1} . . . . . the x-intercepts
__
e) The y-intercept is f(0) = c = -5.
__
f) The vertex was found in part (c) to be (-2, -9).
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.
Answers
This is because of the law of indices which says:
[tex]\sqrt[x]{n}[/tex]= [tex]x^{\frac{1}{m} }[/tex]
So, if we have:
[tex]\sqrt{n}[/tex]
Then the following will be true because of this math law:
[tex]n^{\frac{1}{2} }[/tex]
Side note: The m value can be greater than n and or less than n, but if it is equal the m and n values cancel out.
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
Helppp pleasee ........
Answers
to solve this you just substitute 4 in for x into the equation and solve for y. since negative 3 plus 7 is 4, y=4
Answer:
y=3
Step-by-step explanation:
y = - x +7
x=4
so y = -4 +7
y = 3
Three partners are investing a total of $900,000 to open a garden and landscaping store. Their investments are in the ratio of 2:3:5. .
Answers
Solution:
2+3+5=10
900,000/10=90,000
90,000x2=180,000
90,000x3=270,000
90,000x5=450,000
What is 2x-3y=12 on a graph?
Answers
if a/3=b/2, what are the following ratios?
a+b/b
Answers
Answer:
1
a+1
es posible q hayan doble respuesta
Step-by-step explanation:
Pasos
a+b/b
Divide b entre b para obtener 1.
da
d
(a+1)
La derivada de un polinomio es la suma de las derivadas de sus términos. La derivada de cualquier término constante es 0. La derivada de ax
n
es nax
n−1
.
a
1−1
Resta 1 de 1.
a
0
Para cualquier término t excepto 0, t
0
=1.
1
a+b/b
Divide b entre b para obtener 1.
a+1
Ms. Henderson's plant is 613 inches tall. It is 156 inches taller than Megan's plant.
How tall is Megan's plant?
Answers
Answer:
Megan's plant is 457 Inches tall
Step-by-step explanation:
-2x -3 for x = -3
( Evaluate the following algebraic expression )
Answers
Answer:
well its -2*-3-3 so
-2*-3 is 6-3 is 3
Step-by-step explanation:
Which of the following represents 3 times the sum of 3
and 8?
Answers
Answer:
The expression would be (x + 3)(x - 8) and if we multiplied those together we would get x^2 - 5x - 24
Step-by-step explanation:
Felicia wants to keep her bill under $55. A cell phone provider charges Felicia $50 per month for her plan plus $0.05 per minute of long-distance calls. Which graph correctly shows the number of long-distance minutes Felicia can use this month?
Answers
Answer:
.05x+50=55
100 minutes
Step-by-step explanation:
simplify
.05x=5 (subtract 50 on both sides)
5/.05=x
100=x
she can call for 100 minutes
PLEASE HELP WILL GIVE FULL PONITS! 3. Using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer. (2 points)
Known side: ____________________
Unknown side: ___________________________
4. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? Identify your choice, and then calculate the distance. (4 points: 1 point for the ratio, 2 points for shown work, 1 point for the answer)
Trigonometric ratio (name): ___________________________
Calculation (Show your work):
5. While you're at the top of the tower, you see an ant walking along the edge of the building. If the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? Use the ratio to find the measurement. (4 points: 1 point for the method, 2 points for shown work, 1 point for the answer)
6. Confirm that your answer to question 5 is correct using the Pythagorean Theorem instead of trig ratios. (3 points)
Answers
Answer:
The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.
Step-by-step explanation:
You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x
=> x = 50 m / tan(86°)
x = 50 m / 14.30 = 0.98 m
solve pls brainliest
Answers
Answer:
64%
Step-by-step explanation:
Step 1: Divide 16 by 25
-> [tex]\frac{16}{25}[/tex] -> [tex]0.64[/tex]Step 2: Multiply quotient by 100.
[tex]0.64 * 100[/tex] [tex]6.4 * 10[/tex] [tex]64[/tex] 64%Therefore, 16/25 as a percentage is 64%.
Answer:
Well you can make a proportion
Percentage means ”Out of a hundred”
So you can make a proportion with any fraction Equal to x/100 since
X is the unknown perctange.
in this case it’s 16/25
16/25 = x/100
So cross multiply To solve for X
1600= 25x
x= 64
So 64 Percent
In this case you can use benchmarks. If you do it more or long enough, you’d memorize them.
In this case 25 is a bench mark of 1/4 or 25. 25 goes into 100 4 times so you can multiply 16 by 4 to get your percentage since if you do multiply 4, you have to do it to both the numerator and the Denominator.
so 16/25
16*4= 64
25*4=100
64/100 or 64 percent.
Common benchmarks for percentages
5, 10, 20, 25, 50
5 is always multiply by 20
10 is always multiply by 10
20 is always multiplied by 5
25 is always multiplied by 4
50 is always multiplied by 2
A house has increased in value by 3% each year. It was worth £150000 4 years ago. How much is it worth now? Give your answer to a sensible degree of accuracy. morto
Answers
Answer: 350000
Step-by-step explanation: Hope this helps :) (if wrong please make sure next time add answer that can be picked from it better or if theres no answers maybe give some more detail?)
solve for y: 1/2(4y+6)=4-2(y-6)/3
Answers
Answer:
y = 7/8
Step-by-step explanation:
12y+18=-4y+32
12y+18-18=-4y+32-18
12y=-4y+14
12y+4y=-4y+14+4y
16y=14
16y/16=14/16
y = 7/8
80% of __ is 16 help
Answers
Answer:
80% of 20 is 16.
Step-by-step explanation:
Hello darling, the answer is 20 ^^
Select the correct answer.
What is ?
A.
B.
C.
D.
Answers
Answer:
B. 7 1/2
Step-by-step explanation:
1. To solve this problem, we have to multiply 2 1/2 by the reciprocal of 1/3.
In other words, multiply 2 1/2 by the inverse of 1/3, which is 3.2. (Solving)
[tex]2\frac{1}{2} *3[/tex] [tex]\frac{5}{2} *3[/tex] [tex]\frac{15}{2}[/tex] [tex]7\frac{1}{2}[/tex]Therefore, the answer is B. 7 1/2.
Answer:
its B mark branli.est pls
Step-by-step explanation:
regression and data analysis
Answers
Answer:..
Step-by-step explanation:..
What is x squared = 100
Answers
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
[tex] {x}^{2} = 100[/tex]
❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Answer:
your equation is this... x2 - 100
since you have no x term to the first power you can write 0x... like this
x2 + 0x - 100
Now, what numbers will add to 0 and multiply to -100
The numbers 10 and -10 will
10 + -10 = 0
10 * -10 = -100
therefore
(x - 10)(x + 10) is the way you factor it
Step-by-step explanation:
HELP PLSSS!!!
What is the equation of the line?
A: y=2x+2
B: y= 1/2x -4
C: y=1/2x + 2
D: y=2x-4
GIVING BRAINLY TO CORRECT ANSWER
Answers
Answer:
The answer is C
Step-by-step explanation:
Hope that helps ;)
HELP ME PLZ
Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 3.25 ⋅ 103 seconds?
Part B: Which is the more reasonable measurement of the distance between the tracks on a railroad:
1.435 ⋅ 10−3 mm or 1.435 ⋅ 103 mm? Justify your answer.
Answers
Answer:
salamat po sa
points.
pa
Step-by-step explanation:
branlest
answer
po
