Answer:
Part A) Yes , the triangles are congruent
Part B) The side-angle-side (SAS) theorem
Part C) The perimeter of ∆PQR is
Step-by-step explanation:
Step 1
we know that
The side-angle-side (SAS) theorem, states that: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
so in this problem
Traingle PQR and Triangle STU are congruent by the SAS Theorem
because
m<PQR=m<STU -------> included angle
PQ=TS
QR=TU
Step 2
<u>Find the value of y</u>
we know that
If the triangles are congruent
then
The corresponding sides are equal
so
substitute
so
Step 3
Find the perimeter ∆PQR
Remember that
The perimeter of ∆PQR is equal to the perimeter ∆STU
The perimeter is equal to
substitute the values
Answer:
D
Step-by-step explanation:
note that the values in the domain map to the values in the domain as
- 1 → 2 ( that is 1 + 3 = 2 )
3 → 6 ( that is 3 + 3 = 6 )
5 → 8 ( that is 5 + 3 = 8 )
In each case 3 is added to the value in the domain(x) to obtain the value in the range ( y = f(x) )
Hence f(x) = x + 3 → D
Hey!
Here’s the answer and set up for A
First you need to find the slope. Since the line is parallel to 3x+9. The slope will be the same so the slope will be 3. Next you need to put it in point slope and switch the sign so if it’s positive it’s going to be negative
This is what it will look like using point slope formula
(y+6)=3(X-2)
Then you will distribute the 3
(Y+6)=3x-6
Finally you will subtract the 6 from the left side so
Y=3x-12 will be your line. Now just do the same thing to B!
Hope this helped!!
By finding the roots of the polynomial, we conclude that the correct graph is the second one.
<h3>
Which is the graph of the polynomial?</h3>
Here we have the polynomial:
To identify it, we need to find the roots, we can rewrite the equation as:
And we can rewrite the last part by using the Bhaskara's formula:
Then the roots are:
x = -2
x = 1
Then we rewrite:
So the roots are at x = 0, x = -2, and x = 1.
The graph with these roots is the second graph (top right).
If you want to learn more about polynomials:
brainly.com/question/4142886
#SPJ1
The two numbers are 6 and 10
<em><u>Solution:</u></em>
Let "x" be the smaller number
Let "y" be the larger number
Given that difference between two numbers is 4
larger number - smaller number = 4
y - x = 4 ----- eqn 1
Also given that three times the smaller number is equal to two times the larger less two
three times smaller number = 2 times larger number less two
3x = 2y - 2 ---- eqn 2
From eqn 1,
y = 4 + x --- eqn 3
Substitute eqn 3 in eqn 2
3x = 2(4 + x) - 2
3x = 8 + 2x - 2
x = 6
From eqn 3,
y = 4 + 6 = 10
Thus the two numbers are 6 and 10