Answer:
solve for x in the second equation is correct
Step-by-step explanation:
Here is the complete question
Which first step for solving the given system using substitution results in an equation without fractions?
(2x+6y=7
(6x + 18y = 24.... 2
Solve for x in the first equation,
Solve for y in the first equation,
Solve for x in the second equation
The best equation to she will be equation 2 since all the coefficients are end numbers
Let us make x t subject f the formula from equation 2;
From 2: 6x+18y = 24
Subtract 18y from both sides
6x+18y-18y = 24-18y
6x = 24-18y
Divide through by 6
6x/6 = 24/6 - 18y/6
x = 4-3y.
You can see that the resulting expression of x is not a fraction. Hence solve for x in the second equation is correct
Answer:
A
Step-by-step explanation:
Given
2k² - k - 3
Consider the factors of the product of the k² term and the constant term which sum to give the coefficient of the k- term.
product = 2 × - 3 = - 6 and sum = - 1
The factors are + 2 and - 3
Use these factors to split the k- term
2k² + 2k - 3k - 3 ( factor the first/second and third/fourth terms )
= 2k(k + 1) - 3(k + 1) ← factor out (k + 1) from each term
= (2k - 3)(k + 1) → A
Answer:
C
Step-by-step explanation:
C is the only choice where all given options have different or no coefficients.
Answer:
EF = 20 cm
Step-by-step explanation:
Here, we want to find the length of EF
To do this, we use the principle of similar triangles
The similar triangles we are considering here will be ;
FEA and FBD
when two triangles are similar, the ratio of their corresponding sides are equal
Let us calculate DC first
we can use Pythagoras’ theorem here and it is that the square of the hypotenuse equals the sum of the square of the two other sides
Using the triangle EDC
15^2 = 12^2 + DC^2
DC^2 = 225-144
DC^2 = 81
DC = 9
So the entire length of BD is 9 + 12 = 21 cm
Thus, we have it that;
Let EF be x
so DF = 15 + x
Hence;
BD/DF = AE/EF
21/15+x = 12/x
21x = 12(15 + x)
21x = 180 + 12x
21x-12x = 180
9x = 180
x = 180/9
x = 20 cm
EF = 20 cm
