Answers:
x = 5
m∠C = m∠H = 38 degrees
WORKINGS
Given that ABCD ≅ FGHJ
We know that corresponding angles of two congruent
quadrilaterals are equal
Therefore,
m∠A = m∠F
m∠B = m∠G
m∠C = m∠H
m∠D = m∠I
Given,
m∠C = 9x – 7
m∠H = 5x + 13
Since m∠C = m∠H
9x – 7 = 5x + 13
Add 7 to both sides of the equation
9x – 7 + 7 = 5x + 13 + 7
9x = 5x + 20
Subtract 5x from both sides of the equation
9x – 5x = 5x – 5x + 20
4x = 20
Divide both sides of the equation by 4
4x/4 = 20/4
x = 5
To determine the measures of angle C and angle H
m∠C = m∠H
We know that m∠C = 9x – 7
Since x = 5
m∠C = 9(5) – 7
m∠C = 45 – 7
m∠C = 38
Therefore, m∠C = m∠H = 38 degrees
Answer:
y = (x-0)^2 + (-5) ⇒ y = x^2 - 5
Step-by-step explanation:
The general vertex form of the parabola y = a(x - h)² + k
Where (h,k) is the coordinates of the vertex.
As shown at the graph the vertex of the parabola is the point (0, -5)
So,
y = a(x-0) + (-5)
y = ax^2 - 5
To find substitute with another point from the graph like (1,-4)
So, at x = 1 ⇒ y = -4
-4 = a * 1^2 - 5
a = -4 + 5 = 1
<u>So, the equation of the given parabola is ⇒ y = x^2 - 5</u>
Answer:
B. 3x + y = 4
Step-by-step explanation:
y = -3x + 4
Check:
3x + y = 4
<u>-3x -3x</u>
y = -3x + 4
Answer: Mark has 28 marbles while Don has 85 marbles.
Step-by-step explanation:
Let x represent the number of marbles that Mark has.
Let y represent the number of marbles that Don has.
If Don has 1 more than 3 times the number of marbles Mark has, it means that
y = 3x + 1
The total number of marbles is 113. It means that
x + y = 113- - - - - - - - - - - - 1
Substituting y = 3x + 1 into equation 1, it becomes
x + 3x + 1 = 113
4x + 1 = 113
4x = 113 - 1 = 112
x = 112/4
x = 28
y = 3x + 1 = 3 × 28 + 1
y = 85
Answer:
A) 4
Step-by-step explanation:
There are a couple of ways to get this but this is how I did it:
1. Multiply the second equation by 1/4 to get the same fraction for y as the one in the first equation
1/4 x + 1/8 y = 2
1/4 (1/3 x + 1/2 y = 4)
1/12 x + 1/8 y = 1
2. Subtract the first equation from the new equation
1/12 x + 1/8 y = 1
<u> - 1/4 x - 1/8 y = -2</u>
-1/6 x= -1
3. Divide both sides by -1/6
<u>-1/6</u> x= <u>-1</u>
-1/6 -1/6
x = 6
4. Substitute 4 in for x in the original equation:
1/4 (6) + 1/8y = 2
6/4 + 1/8y = 2
1/8y = 1/2
y = 4
