Cavalieri’s principle states that if two solids of equal height have equal cross-sectional areas at every level parallel to the respective bases, then the two solids have equal volume. the two shaded solids both have a height of 2r units. at every level, the areas of the cross sections of both solids equal π(r2 – b2). a cylinder and a sphere are shown. 2 cones are cut out of the cylinder. the cones have a radius of 4. the cylinder has a height of 2 r. the sphere has a radius of 4. the sphere has a height of 2 r. cross-sectional areas are shown on each figure. therefore, the formula for the volume of the sphere can be derived by writing an expression that represents the volume of one cone within the cylinder. the two cones within the cylinder. the solid between the two cones and the cylinder. the cylinder.

Answer:

See below ~

Step-by-step explanation:

Finding the x-intercepts :

Finding the vertex :

Answer:

x-intercepts:  x = 1 and x = -3

vertex:  (-1, -36)

Step-by-step explanation:

x-intercepts are when y = 0

⇒  9(x + 3)(x - 1) = 0

Divide both sides by 9:

⇒  (x + 3)(x - 1) = 0

Therefore:

⇒  (x + 3) = 0 ⇒ x = -3

⇒  (x - 1) = 0 ⇒ x = 1

Therefore the x-intercepts are x = 1 and x = -3

Vertex form:  [tex]y=a(x-h)^2+k[/tex]  where (h, k) is the vertex

Completing the square

[tex]\begin{aligned}y & =ax^2+bx+c\\& =a\left(x^2+\dfrac{b}{a}x\right)+c\\\\& =a\left(x^2+\dfrac{b}{a}x+\left(\dfrac{b}{2a}\right)^2\right)+c-a\left(\dfrac{b}{2a}\right)^2\\\\& =a\left(x-\left(-\dfrac{b}{2a}\right)\right)^2+c-\dfrac{b^2}{4a}\end{aligned}[/tex]

Therefore:

[tex]y=9(x+3)(x-1)[/tex]

[tex]\implies y=9x^2+18x-27[/tex]

Completing the square to rewrite the equation in vertex form:

[tex]\begin{aligned}y & =9x^2+18x-27\\& =9\left(x^2+\dfrac{18}{9}x\right)-27\\\\& =a\left(x^2+\dfrac{18}{9}x+\left(\dfrac{18}{2(9)}\right)^2\right)-27-9\left(\dfrac{18}{2(9)}\right)^2\\\\& =9\left(x-\left(-\dfrac{18}{2(9)}\right)\right)^2-27-\dfrac{18^2}{4(9)}\\\\& =9(x+1)^2-36\end{aligned}[/tex]

Therefore, the vertex is (-1, -36)

Answer:

B) y = x - 50

Step-by-step explanation:

It is B because the graph's y-intercept lies on the point (0, -50), hence the equation, y = x - 50. In addition, you can verify that B is the correct answer because the slope of the graph is positive, and so the x-value also must be positive.

Answer:

1.cannot

2.can

3.cannot

4.can

Step-by-step explanation:

it's actually quite simple. if the angles add up to 180°, it is a triangle. so if they don't, then its not a triangle.

21+28+41= 90 -> not a triangle

65+45+70=180 -> triangle

48+52+54=154 -> not a triangle

16+40+124=180 -> triangle

Answer:

A)Reduction

B)0.5

Step-by-step explanation:

A)It gets smaller

B)A-D=12

A'-d'=6

6/12=0.5

Step-by-step explanation:

Hello all beautiful your day

Answer:

6.28 meters

Step-by-step explanation:

Circumference is D[tex]\pi[/tex]

D=2 meters

2*3.14 = 6.28

Answer:

2(c-2)=5

Step-by-step explanation:

Twice means to multiply by two. Difference is subtraction, and the difference is between a number (c) and 2. Together, the equation equals 5.

Hope this helps!

With ∠C=∠F, ΔABC and ΔDEF are congruent by AAS congruence. Therefore, option A is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Consider ΔABC and ΔDEF,

Here, ∠B=∠E=50°

AB=DE=10 units

With ∠C=∠F

So, by AAS congruence theorem ΔABC and ΔDEF are congruent

Therefore, option A is the correct answer.

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Answer:

See below ~

Step-by-step explanation:

Anthony has graphed the inequality y ≤ -2x + 1.

For an inequality using a > or < sign, a dotted line has to be used instead of a solid line.

Answer:

3k

Step-by-step explanation:

8k and 5k are "like terms" because they have the same variable to the same degree. So because the are like terms they can be subtracted. Similarly to how 8-5 is 3,

8k - 5k is 3k

Answer:

b=125

Step-by-step explanation

9cm x 14 - 1 = 125

Answer:

the correct answer is A, thats when cos of ttheta is

The value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

Trigonometric ratios are the ratio of sides of a right angled triangle. There are 6 types of trigonometric ratios: sin, cos, tan, cosec, sec, and cot.

Sine trigonometric ratio is the ratio of perpendicular (side opposite to the angle) to the hypotenuse.

In the given figure, the side opposite to the angle [tex]\beta[/tex] is AC = 4 and the hypotenuse is AB = 5.

So, the sine ratio will be equal to,

[tex]\sin \beta=\dfrac{4}{5}[/tex]

Therefore, the value of [tex]\sin \beta[/tex] in the given triangle ABC is [tex]\dfrac{4}{5}[/tex]. Option D is correct.

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And XZ=1/2XY

XZ be x

Now

XZ=21.4units

Answer:

XZ = 21.4 units

Step-by-step explanation:

If  ΔXYZ  is an isosceles triangle then XY = ZY

(the dashes on the line segments indicate they are of equal measure)

If XZ = ¹/₂XY then

⇒ 2XZ = XY = ZY

If the perimeter is 107 units:

⇒ Perimeter of ΔXYZ = XY + ZY + XZ

⇒ 107 = 2XZ + 2XZ + XZ

⇒ 107 = 5XZ

⇒ XZ = 107 ÷ 5

⇒ XZ = 21.4 units

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

Explanation:

We have a triangle with these side lengths

The order of 'a' and b doesn't matter, but we must have c as the largest value. Usually a,b,c are in ascending order.

Plug those values into the formula for the pythagorean theorem. If we get the same thing on both sides, then we have a right triangle.

[tex]a^2 + b^2 = c^2\\\\31^2 + 72^2 = 78^2\\\\961+5184 = 6084\\\\6145 = 6084\\\\[/tex]

We have a false statement at the end, which means the original equation is false for those a,b,c values.

Therefore, we do not have a right triangle.

Instead, this triangle is acute since the [tex]a^2+b^2[/tex] side is larger than the [tex]c^2[/tex] side

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

Rules to have in your notebook or on a reference sheet:

[tex]\text{If }a^2 + b^2 = c^2 \text{ then it is a right triangle}\\\\\text{If }a^2 + b^2 > c^2 \text{ then the triangle is acute}\\\\\text{If }a^2 + b^2 < c^2 \text{ then the triangle is obtuse}\\\\[/tex]

For more information, check out the converse of the pythagorean theorem.

Answer:

Form: (x+5)^2 = 2

Solution: -6.41, -3.59

The length of the SM parallelogram when the length of the rectangle is 15 cm and width is 8 cm is 8/5 units.

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

[tex]A=a\times b[/tex]

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The length of the rectangle is 15 cm and width is 8 cm. Thus, the area of it is,

[tex]A=15\times8\\A=120\rm\; cm^2[/tex]

All three parts has equal area. Thus, the area of parallelogram NCMA is,

[tex]A_p=\dfrac{120}{3}\\A_p=40\rm\; cm^2[/tex]

MN is the height of the parallelogram. Thus,

[tex]A_p=h\times AS\\40=h\times15\\h=\dfrac{40}{15}\\h=\dfrac{8}{5}[/tex]

Thus, the length of the Sm parallelogram when the length of the rectangle is 15 cm and width is 8 cm is 8/5 units.

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Step-by-step explanation:

since he was already on time on the first day, the question is reduced to the probability of being on time on exactly one of the next 2 days.

the probability to be on time on exactly one day means to be on time on one day and to be late on the other.

the probability to be late is the opposite of the probability to be on time, so

1 - 0.7 = 0.3

so, the probability for this combined event for one of the day combinations is

0.7 × 0.3 = 0.21

how many day combinations (1 day on time, the other late) can we have ? 2 (either on time on the first and late on the second, or late on the first and on time on the second).

so, we need to multiply this with the basic probability and get

0.21 × 2 = 0.42

so, b. is the right answer.

Answer: 18x + 15

Step-by-step explanation:

(qor)(x)

q(r(x))

q(6x+5)

3(6x+5)

⇒18x + 15   This is your answer I believe

if we were solving for x then..

⇒x = [tex]-\frac{15}{18}[/tex]

Answer:

x=45, y=45, z= 131

Step-by-step explanation:

x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.

Now that there are 2 right angles, that makes up 180. 180+49=229

A full rotation is 360, so you subtract that. 360-229=131
z=131.

Answer:

Step-by-step explanation:

The relevant relations are ...

__

The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.

  y = 49°

The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.

  x + y = 90°

  x + 49° = 90°

  x = 41° . . . . . . . . . subtract 49°

The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")

  49° +z = 180°

  z = 131° . . . . . . . subtract 49°

The measures of the marked angles are ...

  x = 41°

  y = 49°

  z = 131°

Answer:

Also the quadrilateral shown is a rhombus

Step-by-step explanation:

Answer:

a) 1

b) 0

c) hundreths

d) .8

Step-by-step explanation:

The order, for this problem, is:

hundreds, tens, ones,

then after the decimal

tenths, hundredths, thousandths, ten thousandths, etc.

as for step d, imagine .08 as 8/100, and 8/10. Would you rather have 8 slices of pizza out of 100 slices, or 8 out of 10 slices of the whole?

I hope I helped!

Answer:

∠J = 31.06°

Step-by-step explanation:

Taking the inverse sin function :

Answer:C

Step-by-step explanation:First multiply 5*5=25 then divide 125/5 = 5