Answer:
The<u> rise divided by the run </u>is the slope of a line. The rise and run are used to estimate the slope of a line from its graph.
To determine the intercepts from a graph, We <u>put y equal to zero</u> and solve for x to find the x-intercept. Similarly, we put x equal to zero and solve for y to find the y-intercept.
Answer:
The factored expression is 2(x² + 5)(x + 3).
Step-by-step explanation:
Hey there!
We can use a factoring technique referred to as "grouping" to solve this problem.
Grouping is used for polynomials with four terms as a quick and easy factoring method to remove the GCF and get down to the initial terms that create the expression/function.
Grouping works in the following matter:
- Given equation: ax³ + bx² + cx + d
- Group a & b, c & d: (ax³ + bx²) + (cx + d)
- Pull GCFs and factors
Let's apply these steps to the given equation.
- Given equation: 2x³ + 6x² + 10x + 30
- Group a & b, c & d: (2x³ + 6x²) + (10x + 30)
- Pull GCFs and factors: 2x²(x + 3) + 10(x + 3)
As you'll see, we have a common term with both sides of the expression. This term, (x + 3), is a valuable asset to the factoring process. This is one of the factors for our expression.
Now, we use our GCFs to create another factor.
- List GCFs: 2x², 10
- Create a term: (2x² + 10)
Finally, we'll need to simplify this one by taking another GCF, 2.
- Pull GCF: 2(x² + 5)
Now that we have this term, we need to understand that this <em>could</em> also be factored further using imaginary numbers, but it is also acceptable to leave it in this form.
Therefore, we have our final factors: 2(x² + 5) and (x + 3).
However, when we factor, we place all of our terms together. This leaves us with the final answer: 2(x² + 5)(x + 3).
The daughter will be 24 and the mother would be 48 because 24*2=48.
and are there any answer for the second question
Answer:
Option B is correct.
Step-by-step explanation:
Given: RSTU is a parallelogram.
By definition of parallelogram, two pairs of opposite sides are congruent in length.
⇒
and 
In triangle RST and triangle TUR
[Side]
[Side]
[Common side]
SSS(Side-Side-Side) postulates states that if three sides of one triangle are congruent to three sides of other triangle, then the triangles are congruent.
then, by SSS postulates we have;
Given:
PQRS is a circle, PQT and SRT are straight lines.
To find:
The value of x.
Solution:
Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.
We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.
Now, SRT is a straight line.
(Linear pair)
...(i)
According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.
Using exterior angle theorem in triangle QRT, we get
Therefore, the value of x is 103 degrees.
