Point at (0,-3) and another point at (1,1)....draw a straight line through the points and draw arrows at the end, symbolizing that the line goes to infinity
Answer:
Part 1) Triangles ABC, DBG, DEF and BEH are similar
Part 2)
Step-by-step explanation:
Part 1)
we know that
If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
In this problem Triangles ABC, DBG, DEF and BEH are similar, because its corresponding angles are congruent by AA Similarity Theorem
Part 2)
Remember that
If two triangles are similar, then the ratio of its corresponding sides is equal
therefore
Answer:

k = -4
Step-by-step explanation:
Given system of equations are,
-3x-3y = h
-4x + ky = 10
We have to find the values of h and k such that system of equations has no solution.
The standard form of system of equation in two variables can be given by,


And condition for the system of equations has no solution is given by,

So, by comparing the standard form of equations with given equations, the condition such that system has no solution can be written as,


=> k = -4
and 



So, the value of h and k for above given system of equations is
and k = -4.
Answer:
Inequality: x + 6 ≤ 24
Solution: x ≤ 18
Step-by-step explanation:
<u>Plus</u>: "+" → to <u>add</u> something to something else
<u>Less than or equal to</u>: "≤" → the expression on the left side of the inequality sign is <u>smaller</u> than the expression on the right side of the sign.
Let x be the unknown number.
A number plus 6 is less than or equal to twenty-four:
x + 6 ≤ 24
To solve the found inequality, subtract 6 from both sides:
⇒ x + 6 - 6 ≤ 24 - 6
⇒ x ≤ 18
Therefore, the solution to the inequality is x ≤ 18. The unknown number x can be <u>any real number equal to or less than 18</u>.
Answer:
[x+(4-i)][x+(4+i)]
Step-by-step explanation:
Complete the square then regroup the first two terms. Add and subtract: (b/2)^2=(8/2)^2=16
x^2+8x+17=(x^2+8x)+17
=(x^2+8x+16)+17-16
=(x+4)^2+1 create a difference of squares using i^2= -1
=(x+4)^2 - (-1)
=(x+4)^2 - i^2 use the difference of two squares identity
=[(x+4) - i][(x+4)+i]
=[x+(4-i)][x+(4+i)]