Answer:
the Anser is B and E
Step-by-step explanation:
In equation, (-d + e)( 4e + d) will be (-4ed - d^2 + 4e^2 +ed ) to simplify we combine the terms with the same variables such as d^2, e^2 and ed. The equation becomes, 4e^2 - 3ed - d^2 . The product has 3 terms with a degree of 2. The statements that are true are B and E.
The product of (-d + e)(4e+d) is 4e²-d²-3ed.
The correct option is B and E.
An expression is a combination of numbers, variables, functions such as addition, subtraction, multiplication or division etc.
Given: (-d + e)( 4e + d)
Applying the distributive two times:
= -d*4e-d*d+4e*e+d*e
=-4ed-d²+4e²+ed
=4e²-d²-3ed.
Thus, (-d + e)( 4e + d) = 4e²-d²-3ed.
Hence, The product has 3terms with a degree of 2.
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Answer:
Gym B and Gym A charge the same hourly rate for the children.
Step-by-step explanation:
Answer:
HERE
Step-by-step explanation:
To determine which system has x = 3 and y = 2.5 as its solution, we need to substitute these values into each system of equations and check which one satisfies the conditions.
System 1: 7x - 5y = 33.5
Substituting x = 3 and y = 2.5:
7(3) - 5(2.5) = 21 - 12.5 = 8.5
System 2: 3x + 3y = 1.5
Substituting x = 3 and y = 2.5:
3(3) + 3(2.5) = 9 + 7.5 = 16.5
System 3: 4x + y = 9.5
Substituting x = 3 and y = 2.5:
4(3) + 2.5 = 12 + 2.5 = 14.5
System 4: 5x - y = 12.5
Substituting x = 3 and y = 2.5:
5(3) - 2.5 = 15 - 2.5 = 12.5
System 5: 2x - 5y = 18.5
Substituting x = 3 and y = 2.5:
2(3) - 5(2.5) = 6 - 12.5 = -6.5
System 6: x + y = 5.5
Substituting x = 3 and y = 2.5:
3 + 2.5 = 5.5
System 7: 11x + 10y = 8
Substituting x = 3 and y = 2.5:
11(3) + 10(2.5) = 33 + 25 = 58
System 8: 5x - 2y = -20
Substituting x = 3 and y = 2.5:
5(3) - 2(2.5) = 15 - 5 = 10
From the calculations, we can see that only System 4: 5x - y = 12.5 satisfies the given conditions when x = 3 and y = 2.5. Therefore, the correct answer is System 4.
Answer:
x=5
Step-by-step explanation:
opposite angles are the same, so the small ones are 15. 180-30=150
150/2=75 75/15=5
Answer:
28 ways
Step-by-step explanation:
28 ways
Answer:the center of the sphere is (1/k, 1/k, 1/k) (or (r/k, r/k, r/k) if r is taken as 1), and the radius is sqrt((1 - ka1)^2 + (1 - ka2)^2 + (1 - ka3)^2) / k.
Step-by-step explanation:
The given vector equation, s(r - kx, y, z) = s(r - ka1, a2, a3) = s(r - kb1, b2, b3) - 0, represents a sphere in three-dimensional space. To find its center and radius, we need to analyze the equation.
Let's compare the given vector equation to the standard equation of a sphere:
(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2.
From the given equation, we can identify the following:
1. Center: The center of the sphere can be found by equating the expressions inside the parentheses to zero.
Setting r - kx = 0, we find that x = r/k.
Setting r - ky = 0, we find that y = r/k.
Setting r - kz = 0, we find that z = r/k.
Therefore, the center of the sphere is (r/k, r/k, r/k), or simply (1/k, 1/k, 1/k) if r is taken as 1.
2. Radius: The radius of the sphere can be found by calculating the distance between the center and any point on the sphere.
Considering the points (r - ka1, a2, a3) and (r - kb1, b2, b3), we can calculate the distance between the center (1/k, 1/k, 1/k) and any of these points.
Using the distance formula, the distance between two points (x1, y1, z1) and (x2, y2, z2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).
Therefore, the radius of the sphere is d = sqrt((1/k - ka1)^2 + (1/k - a2)^2 + (1/k - a3)^2), which simplifies to sqrt((1 - ka1)^2 + (1 - ka2)^2 + (1 - ka3)^2) / k.