The mother is 24 years old because her daughter is currently 6 years old and im three years the daught will be 9 and the mother will be 27 years old..
The expression for the area of frame is 4x² + 24x + 35
<h3>What is Area of rectangle?</h3>
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
Here, Old length of photograph = 5 inch
Old width of photograph = 7 inch
Now, length of new photograph = (5 + 2x) inch
width of new photograph = (7 + 2x) inch
Now, Area of frame with new dimension = Length X breadth
= (5+2x) X (7+2x)
= 5(7+2x) + 2x(7+2x)
= 35 + 10x + 14x + 4x²
= 4x² + 24x + 35
Thus, the expression for the area of frame is 4x² + 24x + 35.
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From the picture, we see that there are two congruent sides. Therefore, following the Isosceles Triangle Theorem, if two sides in a triangle are congruent, then the angles opposite those sides are congruent. So, we know that the angles opposite of the congruent sides have an angle measure of x°. We are given the measure of the angle at the top vertex of 100°. Following the Triangle Sum Theorem, the three interior angles in a triangle must sum up to 180°. Therefore, we can create an Algebraic equation to solve for the two base angles that measure x°.
x+100+x=180
x=the base angle measures since they are congruent.
100+x+x=180
Community Property of Addition
100+2x=180.
Added x+x as like terms to = 2x.
100-100+2x=180-100
Subtraction of 100 from both sides to cancel it out and move it.
2x=80
Subtraction operation
2x/2=80/2
Divided by 2 to cancel it out on both sides and move it.
x=40°.
Therefore, the two base angles (angles opposite of the two congruent sides) are 40°.
2(40)+100=80+100=180.
So x=40
Answer:
It is twice the area of a rectangle with sides 2 units × 3 units.
Step-by-step explanation:
