Jamal is stacking boxes of books for the library book sale. Each box contains 24 books. If the stack of boxes is

in the shape of a square-based pyramid, how many books total will there be in a stack of 4 layers?

a. 30

b. 336

c. 28

d. 720

Answer:

52

Step-by-step explanation:

To solve, use the Pythagorean Theorem, which says c² = a² + b². Enter 20 as a and 48 as b and square them both. This will give you 400 for a, and 2304 as b. Add them to get 2704. So, c² = 2704. Find the square root of this to get 52. So, the third side is 52 in length.

Answer:

46800

Step-by-step explanation:

10x15x24x13=46800

Answer:

(1) = (e) 7x. (2) = (b) 7+x. (3) = (d) x-7. (4) = (c) 2x+7

Answer: (b + 3)/2

[tex]\frac{b-5}{2b}.\frac{b^{2}+3b }{b-5}=\frac{b^{2}+3b }{2b}=\frac{b(b+3)}{2b}=\frac{b+3}{2}[/tex]

Step-by-step explanation:

Answer:

(b + 3)/2

Step-by-step explanation:

Answer:

2) Mia needs to buy 3 packages of noisemakers

3)Mia needs to buy 4 packages of hats

4)Mia will dpend a total of $66

Answer:

The measure of the 2 angles are 90° and 35°.

Step-by-step explanation:

The sum of angles in a triangle is 180°.

2x + x - 10 + 55 = 180

Simplify.

3x + 45 = 180

Find 3x.

3x = 180 - 45

    = 135

Find x.

x = 135 ÷ 3

x = 45

2x° = 45° × 2

     = 90°

(x-10)° = 45° - 10°

          = 35°

Answer: x=45

Step-by-step explanation:

2 times 45 is equal to 90

45-10 is equal to 35

55+90+35=180

Answer:

I think the answer is x≥-3

Answer:

number 6 is -8 number 7 is 9 number 8 is 25 and number 9 is -16

Answer:

if you want ans area of cylider is 2πrh+2πr2

Step-by-step explanation:

need thanks and make me brainiest if it helps you

Answer:

Exact Distance = [tex]\frac{4\sqrt{10}}{5}[/tex]

Approximate Distance = 2.529822

============================================

Explanation:

This process is quite involved if you don't know the shortcut formula. I'll go over the long method first, and then show the shortcut in the next section.

First we'll need the equation of the line through points O and M. Use of the slope formula will show line OM has slope -1/3, which you are correct in stating.

Then use point slope form to determine the equation of line OM is y = (-1/3)x+11/3. This converts to the standard form x+3y = 11.

For anything in the form Ax+By = C, the equation perpendicular to this is of the form Bx-Ay = D. The A,B coefficients swap, and one item is negated. This helps form the negative reciprocal slope needed for the perpendicular line.

Compare x+3y = 11 to Ax+By = C. We see that A = 1 and B = 3.

So Bx-Ay = D turns into 3x-y = D. Then plug in the coordinates of H(-3,2) and compute to get

3x-y = 3(-3)-2 = -9-2 = -11. So D = -11

The equation 3x-y = D turns into 3x-y = -11 which is the equation of the line through point H and this line is perpendicular to line OM.

At this point, we have this system of equations

x+3y = 11

3x-y = -11

Solve that system however you wish. Substitution may be the best choice. Doing so leads to the intersection point (-2.2, 4.4)

The last step is to apply the distance formula between the points H(-3,2) and the intersection point (-2.2, 4.4)

The distance you should get is [tex]\frac{4\sqrt{10}}{5} \approx 2.529822[/tex]

I'm skipping steps because listing everything out would take up way too much space in my opinion.

--------------------------------------------------------

The first section goes over a fairly lengthy process of finding the perpendicular distance. Luckily, there's a shortcut.

Consider an equation of the form Ax+By=C, aka standard form. Now consider a point P located at (m,n) that is not on the line Ax+By = C. We can find the distance from P to the line using this formula below

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}[/tex]

In this case, A = 1, B = 3 and C = 11 found back in the previous section. So you'll still need to calculate the equation of line OM.

Also, we'll use (m,n) = (-3,2) which are the coordinates of point H

From here it's a fairly straightforward computation

[tex]d = \frac{|Am+Bn-C|}{\sqrt{A^2+B^2}}\\\\d = \frac{|1*(-3)+3*2-11|}{\sqrt{(1)^2+(3)^2}}\\\\d = \frac{|-8|}{\sqrt{1+9}}\\\\d = \frac{8}{\sqrt{10}}\\\\[/tex]

Optionally we can rationalize the denominator like so

[tex]d = \frac{8}{\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10}\sqrt{10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{10*10}}\\\\d = \frac{8\sqrt{10}}{\sqrt{100}}\\\\d = \frac{8\sqrt{10}}{10}\\\\d = \frac{2*4\sqrt{10}}{2*5}\\\\d = \frac{4\sqrt{10}}{5}\\\\d \approx 2.529822\\\\[/tex]

There are different ways to write down the answer, but they all represent the same number.

Answer:

A

Step-by-step explanation:

not sure gusto ko lang tumulong

Answer:

The length and width of the rectangle are: [tex]\mathbf{2x^5y^8\:and\: 12xy^7}[/tex]

Option A is correct.

Step-by-step explanation:

We are given: [tex]Area\:of\:rectangle=Length\times Width[/tex]

if [tex]Area = 24x^6y^{15}[/tex]we need to find the length and width of rectangle from options given.

Looking at the options, Option B,C and D are incorrect because multiplying the given lengths and widths, the area is not equal to [tex]24x^6y^{15}[/tex]

Only Option A gives us the result i,e

[tex]Area=2x^5y^8\times 12xy^7\\Area=24x^6y^{15}[/tex]

So, the length and width of the rectangle are: [tex]\mathbf{2x^5y^8\:and\: 12xy^7}[/tex]

Option A is correct.

The y-intercept is positive 15

Answer:

I would say A?

Step-by-step explanation:

if i'm not right im sorry :(

Answer:

x = 2

Step-by-step explanation:

5 ( 6x - 4 ) = 20 + 4 ( 3 + x )

30x - 20 = 20 + 12 + 4x

30x - 20 = 32 + 4x

26x = 52

x = 2

Answer:

Wyatt I'm pretty sure so D

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The drawing is a bit unfortunate, as it does not show the angles true to size.

__

When the altitude (EG) of a triangle (∆DFG) is also a median, then that triangle is isosceles. Both halves are congruent right triangles.

  ∆GED ≅ ∆GEF

Since these are right triangles, the acute angle not given (∠EGF) is the complement of the one that is given.

  m∠EGF = 90° -m∠F = 90° -40°

  m∠EGF = 40°

__

Of course, angle D in ∆GED is identical to its counterpart in ∆GEF, angle F, so ...

  m∠D = 40°

__

Because the lines are parallel, angle ABE corresponds (and is congruent) to angle DEG, which is marked as a right angle.

  m∠ABE = 90°

Answer:

The term that can be added to the list so the GCF is 12h3 would be 48h5.

I hope this helped!! :)

Answer:

x = 32, y = 51

Step-by-step explanation:

You know the longest side of ΔTUS is 13m and the longest side of ΔMNP is (2x-y). Thus:

2x - y = 13 --- Equation 1

You know the sum of angles in a triangle is 360°. Two of the angles are given in ΔMNP (142° & 24°) and the remaining angle is (2x-50)°. Thus:

142 + 24 + 2x - 50 = 180

2x + 116 = 180

2x = 180 - 116

2x = 64

x = 64 ÷ 2

x = 32 --- Equation 2

Substitute x = 32 into Equation 1:

2(32) - y = 13

64 - y = 13

-y = 13 - 64

   = -51

y = 51 --- Equation 3

Answer:

x = 32, y = 51

Step-by-step explanation:

Since the triangles are congruent then corresponding angles and sides are congruent, then

∠ U = ∠ N and NP = US

Require to find ∠ N

∠ N = 180° - (24 + 142)° ← sum of angles in triangle

      = 180° - 166°

      = 14°

Thus

2x - 50 = 14 ( add 50 to both sides )

2x = 64 ( divide both sides by 2 )

x = 32

and

NP = US

2x - y = 13 ← substitute x = 32

2(32) - y = 13

64 - y = 13 ( subtract 64 from both sides )

- y = - 51 ( multiply both sides by - 1 )

y = 51

Answer:

16a^2+16a-5

Step-by-step explanation:

set the equations up as a binomial and use FOIL to distribute then add like terms:

(4a+5)(4a-1)

=16a^2-4a+20a-5

=16a^2+16a-5

Answer:

The rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:

(x, y) → (1/2x, 1/2y)

Step-by-step explanation:

Given the vertices of a triangle

After the dilation, the vertices of an image triangle be

If we closely observe, we can notice that the image triangle vertices A'B'C' are half of the original triangle ABC.

i.e. (x, y) → (1/2x, 1/2y)

verification

A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2)

B(2, -4) → B'(2/2, -4/2) = B'(1, -2)

C(0, 2) → C'(0/2, 2/2) = C'(0, 1)

Thus, it is verified and we conclude that the rule which best represents the dilation that was applied to Triangle ABC to create A’B’C’ will be:

Answer: Translate GHJ by the directed line segment GS. Rotate G'H'J' using T as the center by angle H'TS. Reflect G"H"J" over ST

Step-by-step explanation:

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

For a shape to be a parallelogram, the angles that are across from one another have to be equal.

We can now find x by making both equations equal to each other and solving.

[tex]11x+1=13x-5[/tex]

Solve.

[tex]11x+1=13x-5\\6=2x\\x=3[/tex]

Answer:

Step-by-step explanation:

Given the angle ∠AOB

It is stated that CO is the angle bisector of ∠AOB.

Given that ∠AOB = 30°

As we know that the angle bisector bisects the angle into two equal angles.

Thus, the angle bisector CO bisects the angle ∠AOB into two equal angles, which are:

as

∠AOB = 30°

Thus, the two formed angles i.e m∠AOC and m∠BOC by the angle bisector would be half of the angle bisector as the angle bisector bisects the angle ∠AOB into two equal angles.

Therefore,

Answer: Simple Answer.

The simplest way to obtain the minimal floor is to throw an egg from the first floor, then from the second and so on. This way when the egg is finally broken then we will know that this is the floor. This is a reliable algorithm, but in the worst-case scenario it would take 100 throws.

The important thing to notice is that it is the only reliable algorithm when you have only one egg. So you need to start using this algorithm when you break the first egg.

Step-by-step explanation: Intuitive answer.

This way, our first egg should be used to split the 100 floors range into smaller ranges as efficiently as possible. Thus, an intuitive and popular answer is to throw the first egg from 1/n-th of the floors to check. For instance 1/3. Then the algorithm will look like the following:

Throw the egg from 33rd floor. If it breaks, then we check the first 32 floors using the second egg.

Otherwise, we throw the egg from 33 + (67 * 1/3) = 55th floor. If it breaks, then we check floors 34 to 55 using the second egg.

…

Worst case scenario for 1/3 is max(33, 24, …) = 33. This way we might find a perfect n that optimizes the number of throws using some dynamic programming. This is a valuable solution that presents programming thinking, but it is not an optimal solution.

The optimal solution is when all arguments of this max function are equal. How do we achieve it? Looking from the end, the last D(n) is going to be 1, because we will finally get to the point where there is only the single floor for the first egg. Therefore D(n-1) should be equal to 2 because it has one less throw of the first egg.

We see then that the first egg should be thrown finally from the 99th floor, previously from 99–2=97, previously from 97–3=94, 90, 85, 79, 72, 64, 55, 45, 34, 22 and the 9th floor. This is an optimal solution! This way, we need 14 throws in the worst case scenario (the smallest difference is 13, but we had to make one extra throw on the 9th floor).

Simple equation to find the answer is following:

Where f is number of floors. This can be simplified to: min n*n+ divided by 2 greater than f

That is equal to: n=ceil 8f + 1 - 1, divided by 2

Given:

The composite figure.

To find:

The volume of the given composite figure.

Solution:

Given composite figure contains a cuboid and a pyramid.

Length, breadth and height of the cuboid are 8, 6 and 4 respectively.

Volume of a cuboid is

[tex]V_1=length\times breadth\times height[/tex]

[tex]V_1=(8)(6)(4)[/tex]

Length and breadth of the pyramid is same as the cuboid, i.e., 8 and 6 respectively.

Height of pyramid = 10 - 4 = 6

Volume of a pyramid is

[tex]V_2=\dfrac{1}{3}\times length\times breadth\times height[/tex]

[tex]V_2=(\dfrac{1}{3})(8)(6)(6)[/tex]

The volume of composite figure is

[tex]V=V_1+V_2[/tex]

[tex]V=(8)(6)(4)+(\dfrac{1}{3})(8)(6)(6)[/tex]

It can be written as

[tex]V=(\dfrac{1}{3})(8)(6)(6)+(8)(6)(4)[/tex]

Therefore, the correct option is A.