Some of the dimensions of a square pyramid are shown in the diagram. The height of the pyramid is 7.5 meters.

square pyramid

What is the volume of the square pyramid in cubic meters?

Question 8 options:

40 m3

120 m3

360 m3

60 m3

DIGRAM BELOW

The angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

Let there is triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

[tex]a^2 + b^2 -2ab\cos(\theta) = c^2[/tex]

(c is opposite side to angle A)

Consider the diagram attached below.

In the diagram given, we have:

AB = tree with length of 45 ft

AC = cable, with length of 'x' ft (assume)

BC = distance of the base of the cable from the base of the tree of measurement 30 ft.

AD = vertical height of the point A (the top of the tree and cable) from the ground of 'h ft' (assume),

Using the cosine rule for the triangle ABC, taking:

|AC| = x = length of the side opposite to the known angle

|AB| = 45 ft and BC = 30 ft are rest of the two sides,

Angle opposite to AC is of 86°

Thus, we get:

[tex]45^2 + 30^2 -2(30)(45)\cos(86^\circ) = x^2\\\\2925 - 188.34 \approx x^2\\\\x \approx \sqrt{2736.66} \approx 52.31 \: \rm ft[/tex]

(took positive root because of x being length, which is a non-negative quantity).

For triangle ABD, using the sine ratio from the perspective of angle A, we get:
[tex]\sin(m\angle A) = \dfrac{\text{side opposite to A}}{\text{length of hypotenuse}} \\\\\sin(86^\circ) = \dfrac{h}{45}\\\\h = \sin(86^\circ) \times 45 \approx 44.89 \: \rm ft[/tex]

Now, for the triangle ACD, using the sine ratio from the perspective of angle C (smaller than 90°), we get:

[tex]\sin(m\angle C) = \dfrac{\text{side opposite to C}}{\text{length of hypotenuse}} \\\\\sin(\theta^\circ) = \dfrac{h}{x} \approx \dfrac{44.89}{52.31} \approx 0.858\\\\\theta =\sin^{-1}(0.858) \approx 59.09, 120.90[/tex]

Taking the angle smaller than 90°, we get:

[tex]\theta \approx 59.09^\circ \approx 59^\circ[/tex]

Thus, the angle (less than 90°) that the cable makes with the ground for this considered case is 59° approximately.

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Answer:

That wasn't the correct answer

Step-by-step explanation:

c^2=45^2+30^2 - 2(45)(30)*Cos(94

c^2=2925+188.3425

c^2=3113.3425

take the square root:

c is approx. 55.8

sin86/55.8=sinx/45

55.8sinx=45sin94

divide both sides by 55.8

sinx=0.8045

sin^-1(0.8045)=53.6

Answer is 53.6 or "L" on the scavenger hunt worksheet

Answer:

Step-by-step explanation:

In rectangle, the diagonals are equal  bisect each other.

⇒ OA = OB

⇒ΔAOB is an isosceles triangle.

In ΔAOB,

x + x + 120 = 180°

  2x + 120 = 180

           2x = 180 -120

           2x = 60

             x = 30°

In ΔABD

∠A + ∠ABD ∠BDA = 180

90  + 30 + ∠BDA  = 180

                 ∠BDA = 180 - 90 -30 = 60°

ΔABD is 30 - 60 - 90 triangle.

The ratio of sides of 30-60-90 triangle is x : x√3 : 2x

x →shortest leg which is opposite ot 30°

∵ x = AD =  20

x√3 → longest leg which is opposite to 60°

x√3 ( AB) = 20*1.732

            AB   = 34.64

Area of rectangle = length * width

                              = 34.64 *20

                             = 692.8

                             ≈ 693 square units

Answer:

Step-by-step explanation:

Remark

All triangles are made up of 3 angles totally 180 degrees.

In addition a right triangle has a measurement of 90 degrees.

The other two angles must add to 90 degrees as will. That is the definition of complementary. (2 angles add to 90 degrees).

Formula

x + 28 = 90

Solution

x + 28 = 90              Subtract 28 from both sides.

x+28 -28=90 - 28

x = 62

The measure of the second angle is 62

Answer:

The Answer is C. 50

Step-by-step explanation:

To pack 600 granola bars, 50 boxes are needed.

The correct option is C.

To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.

Number of boxes = Total granola bars / Granola bars per box

Number of boxes = 600 / 12

Number of boxes = 50

So, 50 boxes are needed to pack 600 granola bars.

The correct answer is option C: 50.

To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.

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Step-by-step explanation:

12(5 + 3x) + 18

60+36x+18

C)36x+78

A=(1/2)(b1+b2)h =

=(48x+68)in² = (1/2)( b1+(9x+12))8

=b1= 3x+5

Answer:

its B

Step-by-step explanation:

Answer:

the answer is B 1/50. I think

Answer:

2.3<x<8.7

Step-by-step explanation:

Answer:

0.0016

Step-by-step explanation:

Hope this helps!

Answer:

8/75 is the answers for the question

Answer:

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.

Answer:

12

Step-by-step explanation:

Length of a circle = circumference = 2πr = 24π

                                            Radius (r) = 24π/2π

                                                             = 12cm

Answer:

wheres the question ?

Step-by-step explanation:

Answer: 10m +27

Step-by-step explanation: Add all the sides together to calculate Perimeter.

2(2m +10)+2m+7+2m +2m

4m + 20 + 2m +7 +2m +2m

10m +27

Answer:

6 tomato plants

Step-by-step explanation:

[tex]18\frac{1}{6}= \frac{18\times6+1}{6}=\frac{108+1}{6}= \frac{109}{6}[/tex]

[tex]2\frac{2}{3}= \frac{2\times3+2}{3}=\frac{6+2}{3}= \frac{8}{3}[/tex]

then the number of tomato plants that Jordan will be able to put a fence around using this roll :

[tex]\frac{\frac{109}{6}}{\frac{8}{3}}= \frac{109}{6}}\times\frac{3}{8} = \frac{109}{2}}\times\frac{1}{8}= \frac{109}{16} = 6.8125[/tex]

then he can put fence only around 6 plants.

Answer:

[tex] - 8x {}^{2} - 6x + 35 [/tex]

Step-by-step explanation:

(2x+5)(7-4x)

expanding

2x(7-4x)+5(8-4x)

removing brackets

2x×7+2x×-4x+5×7+5×-4x

14x-8x^2+35-20x

arranging properly

-8x^2-6x+35

Answer:

Third option

Step-by-step explanation:

The y-intercepts are -2 and 3 so first option is wrong

One is dashed line and other is solid so one needs to have equal and other one shouldn't, so second option is wrong as both are less than but not also equal

Third option the -2 intercept one is less than or equal to And the slope is positive while the 3 intercept one is greater with negative slope.

The given graph represents the system of inequalities in the third option y ≤ 2x - 2 and y > -x + 3.

It is clear from the graph that one of the inequality has a solid graph line while other has a dotted graph line.

So one of the inequality must be of the form ≤ or ≥ and the other one is of the form < or >.

The only inequalities of this form in the options are,

y ≤ 2x - 2

y > -x + 3

Consider y = 2x - 2.

The points through the line are (0, -2), (1, 0), (2, 2), ...

At origin, (0, 0), 0 ≤ -2 is false. So (0, 0) does not include in the solution region.

So the solution region of y ≤ 2x - 2 is on the part of the line of y = 2x - 2 where (0, 0) is not included.

Consider y = -x + 3

Line passes through (0, 3), (1, 2), (2, 1), (3, 0),....

At (0, 0), 0 > 3, which is false.

So the solution region of y > -x + 3 does not contain the part where (0, 0) is included.

So the resulting graph is correct for this system of inequalities.

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Answer:

Step-by-step explanation:

Solution:

Volume of the rectangular prism formula:

[tex]: \Longrightarrow \sf{V=l*w*h}[/tex]

Given:

Then, you multiply.

[tex]\sf{32*10*16=\boxed{\sf{5120}}[/tex]

Answer:

D

Step-by-step explanation:

Probably between obtuse angle or triangle because sometimes they trick you

But I'm not 100 percent sure

Answer:

It is right

Step-by-step explanation:

Right triangles will always form a corner like an L shape

Answer:

1/18

Step-by-step explanation:

probability of getting a three= 1/6

probability of getting a three on a wheel=1/3

probability of winning= 1/6x1/3=1/18

The possible number of different phone numbers will be 128000000

The extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.

In this exercise we have to use the knowledge of probability to find the phone number, so:

1 280 000 000 different ways.

First we have to establish some information about this exercise such as:

Thus, now calculating the possibilities of occurrence, we have:

[tex]8\times 2\times 10=160[/tex]

[tex]8\times 10^6=8000000[/tex]

[tex]160\times 8000000=1280000000[/tex]

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Answer:

[tex]\sf\:Negative = \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}\\\sf\: Positive = \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Step-by-step explanation:

[tex]4 - 3 \sec ^ { 2 } \theta = 0[/tex]

Let's solve this.

Isolate sec²θ.

[tex]4 -3 \sec ^ { 2 } \theta = 0\\- 3 \sec^{2}\theta = -4\\3 \sec^{2}\theta=0\\\sec^{2} \theta=\frac{4}{3}[/tex]

Now, we now that, cos θ is the reciprocal of sec θ. Therefore,

[tex]\sec^{2}\theta = \frac{4}{3}\\\cos^{2}\theta = \frac{3}{4}[/tex]

Bring the square root on both the sides of the equation to remove the square.

[tex]\sqrt{\cos^{2}\theta} = \sqrt{\frac{3}{4} }\\\cos^{2}\theta = (+/-) \frac{\sqrt{3} }{2}[/tex]

If,

[tex]\cos\theta = + \frac{\sqrt{3}}{2}\\= cos \left( \frac{\pi}{6} \right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

Also if,

[tex]\cos\theta = -\frac{\sqrt{3}}{2}\\= \cos \left(\pi - \frac{\pi}{6}\right)\\= \cos \left({\frac{5\:\pi}{6}\right)\\\Longrightarrow \boxed{\sf\:\theta =\pi n_{1}+\frac{5\pi }{6}\text{, }n_{1}\in \mathbb{Z}}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

9 x 2/8 = 9/4

Step-by-step explanation:

Answer:

Step-by-step explanation:

9 divided by 2/8 but make the 2/8 into a decimal and the turn back to a fraction if it ask if not then leave it how it is and if you have to round which you prolly wont have to but ask to make sure ight

Answer:

x=6

Step-by-step explanation:

(I don't know if you mean question 2 3x= 18 or 2 times 3x = 18)

2.3x = 18
3x = 18 / 2 = 9
x = 9/3 = 3

Or : x = 18/3 = 6

Answer:

rotation

Step-by-step explanation:

reflection

Answer:

rotation then translations-- C

Step-by-step explanation:

yes. and bc taking the quiz rn

Answer:

-3

Step-by-step explanation: