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Answer:
the explicit formula for the geometric sequence 2,6,18,54 is
2,6,18,54
Step-by-step explanation:
In the sequence given: 2,6,18,54
The common ration is 3 because
a₁ = 2
a₂= 2*3 =6
a₃ = (2*3)*3 = 2*3^2 = 18
a₄= (2*3*3)*3 =2*3^3 = 54
Here we see for a₂ 3 has power 1, for a₃ 3 has power 2 and so on.
So, the formula will be
Here aₙ is the no of term.
a₁ is the first term of the sequence
and r is the common ratio among the sequence.
9514 1404 393
Answer:
y +2 = (1/4)(x +1)
Step-by-step explanation:
The given line is in slope-intercept form:
y = mx + b
where the slope (m) is -4 and the y-intercept (b) is +13.
For the perpendicular line, we need a slope that is the opposite reciprocal, or ...
-1/m = -1/(-4) = 1/4
A suitable form for the desired equation is the point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
For m=1/4 and (h, k) = (-1, -2), the equation of the line is ...
y +2 = (1/4)(x +1)
Answer:
The correct option is;
∠ADB ≅ ∠CDB, ≅
and
≅
. So ΔABD ≅ ΔCDB by SAS
Step-by-step explanation:
The given parameters are;
The polygon given = Quadrilateral
The diagonal of the quadrilateral = BD
The length of the side AD = (2×y + 5) units
The length of the side CD = (y + 10) units
The given measure of ∠ABD = (2 × y + 25)°
The given measure of ∠CBD = 35°
When y = 5, we have by substituting the value of y into the equations representing the dimensions of the quadrilateral ABCD;
The length of the side AD = 2 × y + 5 = 2×5 + 5 = 15 units
∴ The length of the side AD = 15 units
The length of the side CD = (y + 10) units = (5 + 10) units = 15 units
∴ The length of the side CD = 15 units
The measure of ∠ABD = (2 × y + 25)° = (2 × 5 + 25)° = 35°
The measure of ∠ABD = 35°
Therefore;
∠ADB ≅ ∠CDB by substitution
≅
by reflexive property
≅
by substitution
∴ ΔABD ≅ ΔCBD by Side-Angle-Side rule of congruency
