Answer: x = 22
Explanation:
1) Corresponding sides and correspoding angles of congruent triangles are equal.
2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.
That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:
- ∠A and ∠D are congruent
- ∠B and ∠ E are congruent
- ∠C and ∠F are congruent
- Segment AB and segment DE are congruent
- Segment BC and segment EF are congruent
- Segment AC and segment DF are congruent
In the figures, it is given that the segment DF measures (1/2)x - 1 and the corresponding segment AC measures 10 units.
Hence, you set this equation: (1/2)x - 1 = 10
Solving for x:
- (1/2)x = 10 + 1
- (1/2)x = 11
- x = 2(11)
- x = 22 ← answer
Answer:
3y= -2x-6
Step-by-step explanation:
The two points on the line are (-3,0) and (0,-2)
so you first get the gradient;
gradient= <u>change in y</u>
change in x
= <u>-2-0</u>
0-(-3)
=<u> -2</u>
3
so the answer above is the gradient
then pick one point that you used to get the gradient with, so as for me I'll pick (-3,0) and then a general point which is always (x, y)
since you have the gradient you can easily get the equation by doing this
<u>y-0</u><u>. </u><u> </u> = <u>-2</u>
x-(-3). 3
then crossmultiply to get the equation of the line
3y= -2(x+3)
3y= -2x-6
Answer:
2 1/2 miles per gallon
Step-by-step explanation:
So to travel 8 3/4 miles, we need 3 1/2 gallons of gas. All we need to do is divide the gallons of gas by miles. So we would do 8 3/4 divided by 3 1/2. 3 1/2 goes into 8 3/4 2 1/2 times.
Answer:
y = 
x² - x + 
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, 3 ), thus
y = a(x - 1)² + 3
To find a substitute (- 1, 5) into the equation
5 = a(- 1 - 1)² + 3 ( subtract 3 from both sides )
2 = 4a ( divide both sides by 4 )
a = , thus
y = (x - 1)² + 3 ← expand factor using FOIL
y = (x² - 2x + 1) + 3 ← distribute parenthesis
= x² - x + + 3
= x² - x +
