Find the surface area of the regular pyramid.

Answer:

[tex]b = 74^o[/tex] --- acute base

Step-by-step explanation:

Given

See attachment for the figure

Required

The acute base angle of the trapezoid

From the question, the isosceles triangle and the trapezoid share the same base.

Represent the base angle with b.

So:

[tex]b + b + 32^o = 180^o[/tex] --- angles in a triangle

[tex]2b = 180^o-32^o[/tex]

[tex]2b = 148^o[/tex]

Divide by 2

[tex]b = 74^o[/tex]

9514 1404 393

Answer:

  Part A: 2 ft²

  Part B: draw a diagonal (AC, for example); 1 ft²

Step-by-step explanation:

Part A:

The area of a parallelogram is given by the formula ...

  A = bh

where 'b' is the length of the base, and 'h' is the perpendicular distance between the bases.

Using the numbers shown on the diagram, the area is ...

  A = (3 ft)(2/3 ft) = 3·2/3 ft²

  A = 2 ft² . . . . . area of the parallelogram

__

Part B:

Typically, a polygon is partitioned into triangles by drawing diagonals from one of the vertices. It does not matter which one. (In a quadrilateral, only one diagonal can be drawn from any given vertex.) Here, the "base" of each triangle is the same as the base of the parallelogram: 3 feet. The "height" of each triangle is the same as the height of the parallelogram: 2/3 ft.

The area of a triangle is given by the formula ...

  A = 1/2bh

  A = 1/2(3 ft)(2/3 ft) = (1/2)(3)(2/3) ft²

  A = 1 ft² . . . . . . . . area of each triangle

_____

Additional comment

It should be no surprise that the area of each of the two congruent triangles is 1/2 the area of the parallelogram.

Answer:

20%

Step-by-step explanation:

Decrease in amount = original - new amount

Decrease in amount = 110 - 88 = $22

Decrease % = decrease/original x 100%

= 22/110 x 100%

= 20%

Answer:

this is the correct answer

Answer:

x ≥ −3

Step-by-step explanation:

Step One : Add 9 to both sides.

x − 9 + 9 ≥ −12 + 9

x ≥ −3

There is no more to be done, that is our answer. x ≥ −3.

Hope this helps, please mark brainliest! :)

9514 1404 393

Answer:

  x ≈ 2.87

Step-by-step explanation:

We  can subtract 6 to put the equation into a form easily solved.

  x^2 +2x +1 = 15

  (x +1)^2 = 15

  x +1 = √15 . . . . . for the greatest solution, we only need the positive root

  x = √15 -1 ≈ 2.87

Answer:

[tex]f(20) =3.25[/tex]

Step-by-step explanation:

Given

[tex]f(m) = 1.25 + 0.10m[/tex]

Required

[tex]f(20)[/tex]

We have: [tex]f(m) = 1.25 + 0.10m[/tex]

Substutute 20 for m

[tex]f(20) =1.25 + 0.10*20[/tex]

[tex]f(20) =1.25 + 2[/tex]

[tex]f(20) =3.25[/tex]

Answer:

72

Step-by-step explanation:

12 * 6 = 72

of course, IRL not every problem takes the same amount of time

Answer: if they are all algebra questions then 72

Step-by-step explanation:

12 + 12 + 12 + 12 + 12 + 12= 70

Answer:

[tex]\text{B) }56\:\mathrm{cm^2}[/tex]

Step-by-step explanation:

The area of a triangle with height [tex]h[/tex] and base [tex]b[/tex] is given by [tex]A=\frac{1}{2}bh[/tex]. By definition, the base and the height must intersect at a 90 degree angle. Therefore, the diagram gives a base of 14 cm and a height of 8 cm. Substituting these values, we get:

[tex]A=\frac{1}{2}\cdot 8\cdot 14=\boxed{\text{B) }56\:\mathrm{cm^2}}[/tex]

Step-by-step explanation:

{2,3,5,7,9,11,13,15,17,19}

Answer:

29

Step-by-step explanation:

tan c = opposite / adjacent

c = tan -1 (25/45) = 29

Answer:

Step-by-step explanation:

tan C = opp/adj

sin C = 25/45

sin C = 0.5556

C = sin^-1 0.5556

= 33.75

Answer:

Step-by-step explanation:

81x² - 6x

Answer:

81x² - 6x

Step-by-step explanation:

81x² - 6x

Answer:

x = 3

Step-by-step explanation:

Given :

AE = 3, EB = 4, CE = x, and ED = x +1,

Equating chord AB and CD

AE*EB = CE*ED

3*4 = x*(x+1)

12 = x² + x

x² + x - 12 = 0

x² +4x - 3x - 12 = 0

x(x + 4) - 3(x + 4)

(x + 4) = 0 or (x - 3) = 0

x = - 4 or x = 3

Distance can't be negative :

x = 3

Answer:

CE = 3

Step-by-step explanation:

Given:

AE = 3

EB = 4

CE = x

ED = x + 1

Required:

CE

Solution:

First we need to determine the value of x by generating am equation as follows:

CE × ED = AE × EB (Interacting Chords Theorem)

Substitute

x × (x + 1) = 3 × 4

x² + x = 12

Subtract 12 from each side

x² + x - 12 = 12 - 12

x² + x - 12 = 0

Factorize to find the value of x

x² + 4x - 3x - 12 = 0

x(x + 4) -3(x + 4) = 0

(x - 3)(x + 4) = 0

x - 3 = 0

x = 3

Or

x + 4 = 0

x = -4

Let's use the positive value of x

CE = x = 3

Answer:

p would be up top on the negative side (left)

q would be at the bottom on the positive side (right)

Answer:

[tex]\text{D. }1,920}\:\mathrm{in^3}[/tex]

Step-by-step explanation:

The volume of a rectangular prism is given by [tex]A=l\cdot w\cdot h[/tex], where [tex]l[/tex] is the length of the prism, [tex]w[/tex] is width, and [tex]h[/tex] is height.

Therefore, the area of the given prism is equal to [tex]8\cdot 12 \cdot 20=\boxed{\text{D. }1,920\:\mathrm{in^3}}[/tex].

Answer:

12.7 cm

Step-by-step explanation:

We can obtain CB using Pythagoras :

CB = √12² - 6²

CB = √108

CB = 10.39

Using CB,

We can apply trigonometry on triangle BCD to obtain the length of CD

Sin θ = opposite / hypotenus

Sin 55 = CB / CD

Sin 55 = 10.39 / CD

CD = 10.39 / sin 55

CD = 12.68

CD = 12.7 cm

Answer:

L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]

Step-by-step explanation:

f ( t ) = 10 cos ( 12t + 60°) u(t)

attached below is a detailed solution of the given problem

L(f(t)) = [tex]\frac{5s - 60\sqrt{3} }{s^2 + 144}[/tex]

Answer:

20.51ft

Step-by-step explanation:

Given data

Length= 15ft

Width= 14ft

Height= 8ft

Because we want to find the diagonal, let us use the Length and the width

We can get the diagonal by applying the Pythagoras theorem

z^2= x^2+y^2

z^2= 15^2+ 14^2

z^2= 225+ 196

z^2= 421

square both sides

z= √421

z=20.51 ft

Hence the diagonal is 20.51ft

Answer:

correct answer is c

Step-by-step explanation:

2.44x10^-3

Answer:

y=2x-1

Step-by-step explanation:

Answer:

13,956,779.6764

Answer:

13956 779.7 (•‿•) this is my ans.

Answer:

D

5 sq.rt. 3

Step-by-step explanation:

use the pythagorean theorem: a^2 + b^2 =c^2

5^2 + x^2 = 10^2

25+ x^2 =100

x^2 = 100 - 25

x^2 =75

x = [tex]\sqrt{75}[/tex]

x = 5 [tex]\sqrt{3}[/tex]

We're given the one-sided limit,

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}[/tex]

Evaluating the limand directly at x = 1 gives the indeterminate from

(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0

so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives

[tex]\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}[/tex]

Answer:

D. No; the graph fails the vertical line test.

Step-by-step explanation:

If any vertical line intersects a graph more than once it is NOT a function

Answer:

100

Step-by-step explanation:

482 ÷ 5 = 96.4

96.4 -> 100

Hope this helps! Brainliest?

Answer:

Quotient: 96

Step-by-step explanation:

482/5= 96R2

Quotient: 96

Remainder: 2