Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations? Line y = 5x + 6 intersects line y = −x − 7.
Lines y = 5x + 6 and y = −x − 7 intersect the x-axis.
Lines y = 5x + 6 and y = −x − 7 intersect the y-axis.
Line y = 5x + 6 intersects the origin.
Answers
y = −x − 7
5x + 6 = -x - 7
6x + 6 = -7
6x = -13
x = -13/6
y = 5(-13/6) + 6
y = -29/6
The solution is (-13/6, -29/6) and that tells us that the two ines do not intersect at the origin or any of the two axis. If they intersected at the origin, then the solution should have been (0, 0). If they intersected at the x-axis, the solution should have been (x, 0). If the two lines intersected at the y-axis, the solution would have been (0, y).
The answer is A) Line y = 5x + 6 intersects line y = −x − 7.
Answer:
The answer is A. Line y = 5x + 6 intersects line y = −x − 7.
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Answers
Step-by-step explanation:
as I can see this the answer is
x = 25/78
in decimal
x = 0.320
Final answer:
The problem involves joint variation with variables y, x, and z. After finding the constant of variation, we substitute the given values into the joint variation equation and determine that x = 16.67
Explanation:
First, we establish the equation of joint variation, which in this context is y = kxz, where 'k' is the constant of variation. When y=13, x=26, and z=6, we insert these values into the equation to solve for 'k'. This gives us k = y/(xz) = 13/(26*6) = 0.08333.
Now that we have the constant 'k', we can find the value of 'x' when y=25 and z=18. We rearrange our equation to solve for 'x', resulting in x = y/(kz). Substituting the known values, we get x = 25/(0.08333*18) = 25/1.5 = 16.67. Therefore, if y varies jointly with x and z, and y=25 when z=18, then x = 16.67.
Learn more about Joint Variation here:
#SPJ2
Answers
32-6x+7x=-15+38
32+x=23 /-32 (subtract 32 both sides)
x=-9 - its the resuylt
8g^2 + 3g − 4, the rate that the pool is filled, and 9g^2 − 2g − 5, the rate that water leaves the pool, where g represents the number of gallons entering
or leaving the pool per minute.
a. Write an expression that determines the height of the water in the pool.
b. What will be the height of the water if g = 1, 2, 3, and 4?
c. To the nearest tenth, at which value for g will the water reach its
greatest height? Explain.
Answers
b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5
g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7
g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5
c) Greatest height
Find the vertex of the parabole
The vertex is at the mid point between the two roots.
To find the roots you can use the quadratic equation
The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2
The middle poin is 5/2 = 2.5
Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3
384,400
5,437,200,184,400
Answers
2. 3 hundred thousand value 300,000
Answers
(A) 4 mph
(B) 5 mph
(C) 6 mph
(D) 30 mph
Answers
Answer:
(C) 6 mph
Step-by-step explanation:
Given,
The time taken by Tobin = 30 minutes,
While, the time taken by her opponent = 45 minutes,
So, the ratio of the time taken by tobin and her opponent = 30 : 45
Thus, the ratio of speed of tobin and her opponent =
= 45 : 30
= 3 : 2
Suppose speed of tobin = 3x and speed of opponent = 2x
Where, x is positive real number,
Difference in speed = 3x - 2x = x
According to the question,
x = 2 miles per hour,
Hence, the speed of Tobin = 3x = 6 miles per hour.
Option (C) is correct
d = ( x + 2) *30 Tobin
x * 45 = ( x + 2) *30
x* 15 = 60
x = 4
x + 2 = 6 mph