Luke tried to use Cavalieri's principle to show that the two figures have the same volume. The base areas are the same. Therefore, corresponding cross-sections have the same area. The prisms have the same height. So the volumes must be the same. What is the first mistake Luke made?

Answer:

-375.5<1200

True

Step-by-step explanation:

100-475.5 = -375.5

Brainliest please!!

Answer:

Step-by-step explanation:

a) x(x+12) + 27
b) m(2n-3k) - 2p(3k + 2n)

Answer:

[tex]\mathrm{No\:Solution}[/tex]

Step-by-step explanation:

[tex]\begin{bmatrix}Y=3x-2\\ Y-3x=4\end{bmatrix}[/tex]

[tex]\mathrm{Substitute\:}Y=3x-2[/tex]

[tex]\begin{bmatrix}3x-2-3x=4\end{bmatrix}[/tex]

[tex]\mathrm\:{Combine\:like\:terms:[/tex]

[tex]\begin{bmatrix}-2=4\end{bmatrix}[/tex]

[tex]-2=4\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}[/tex]

[tex]\mathrm{No\:Solution}[/tex]

Answer:

  c.

Step-by-step explanation:

The graph will be shaded above the boundary line when the inequality is of the form ...

  y > ( )

The boundary line will be solid when the comparison includes the "or equal to" case:

  y ≥ ( )

__

Here, the parabola will open upward if the leading coefficient is positive:

  y ≥ x² + ( )

The shading above the solid line tells you the inequality is ...

  y ≥ ( ) . . . . . matches choice C

_____

Additional comment

The parent function x² is shifted left 2 units, so the graph is of (x +2)². The expanded form of this matches choice C.

Answer:

3 is rational, 5 is rational, 1 is rational, 9 is rational, 4 is rational, 8 is rational.

Step-by-step explanation:

Answer:

1.9 years

Step-by-step explanation:

There are 365 days in a year

694.44 / 365 = 1.9

Hope this helps!

Answer:  1.9013

Step-by-step explanation:

Answer:

54 units

Step-by-step explanation:

        We can graph the vertices given to make this easier to solve.

-> See attached.

-> This will help us in finding the lengths of the sides.

-> We can also use mathematics.

8 + 5 = 13 and 8 + 6 = 14

        Next we will find the perimeter.

-> This can be found with either of these formulas:

[] P = 2L + 2W

[] P = W + W + L + L

P = 2L + 2W

P = 2(14) + 2(13)

P = 54

The perimeter of the county is 54 units

Answer:

∠ D = 110°

Step-by-step explanation:

Assuming the quadrilateral is a parallelogram.

• Consecutive angles sum to 180° , then

∠ B + ∠ C = 180 , that is

5x + 3x + 4 = 180

8x + 4 = 180 ( subtract 4 from both sides )

8x = 176 ( divide both sides by 8 )

x = 22

Then

∠ B = 5x = 5 × 22 = 110°

• Opposite angles are congruent

∠ D = ∠ B = 110°

Answer:

Point I is on line segment HJ; which means HI and IJ are equal.

HJ = 15

IJ = 10

Finding the length of HI, given the above statements:

Length of HI = 10 (reason: HI and IJ are congruent)

Answer: The salesperson must sell 20 memberships to make the same amount of money under both plans.

Step-by-step explanation:

Let x be the number of memberships.

In first plan,

Weekly salary of $300 plus a commission of $15 for each membership sold.

i.e. Earning (weekly) = 300+15x

In second plan,

The other plan offers no salary but pays $30 commission on each membership sold.

i.e. earning = 30x

According to the question, when [tex]300+15x=30x[/tex]

[tex]\Rightarrow\ 300=30x-15x\\\\\Rightarrow\ 300=15x\\\\\Rightarrow\ x=\dfrac{300}{15}\\\\\Rightarrow\ x=20[/tex]

Hence, the salesperson must sell 20 memberships to make the same amount of money under both plans.

Answer:

Exact volume = 30,000 + 5,000pi cubic mm

Approximate volume = 45,700 cubic mm

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

Explanation:

Break the figure into two pieces.

The top part is a half-cylinder with radius r = 20/2 = 10 mm and height h = 100 mm.

The volume of this half-cylinder is

V = 0.5*(full cylinder volume)

V = 0.5*pi*r^2*h

V = 0.5*pi*10^2*100

V = 5000pi

This is exact in terms of pi.

The lower part is a 20 mm by 100 mm by 15 mm rectangular block. It has volume of length*width*height = 20*100*15 = 30,000 cubic mm.

---------

We'll add the two volumes found earlier to get the overall volume.

The total exact volume is 30,000+5,000pi cubic mm.

To get an approximation, you can use something like pi = 3.14

30000+5000pi = 30000+5000*3.14 = 45,700 cubic mm is the approximate volume when using pi = 3.14

Answer:

x=37

y=125

Step-by-step explanation:

97+28+x+18=180 (sum of the interior angles of a triangle is 180)

143+x=180

x=180-143

x=37

y+x+18=180 (sum of the angles on a straight line is 180°)

y+37+18=180

y+55=180

y=180-55

y=125

or

y=97+28(exterior angle of a triangle= 2 interior opposite angles)

y= 125

Answer:

G. [tex] C = 25(p - 2) + 439 [/tex]

Step-by-step explanation:

Amount paid by customer to fly to California if carrying 2 pieces or less than 2 pieces of luggage for which they won't be charged for = $439

Fee for additional luggage = $25

Fee for additional luggage if an individual carries p luggages = 25(p - 2)

Total amount (C) if p pieces of luggage were carried by a customer travelling = fee for additional p pieces of luggage + $439

The function for this would be:

[tex] C = 25(p - 2) + 439 [/tex]

Answer:

Step-by-step explanation:

answer: 0.73 because 7 hundreths times 10 = 7 tenths

Answer:

132

Step-by-step explanation:

180-48= 132

Its this bc a straight line is 180 degrees and if you know 48 then its 132+48 which gets 180

Answer:

386% is the 1 3/4 and the other is 239% I think?

Step-by-step explanation:    

not an answer but I’m working on the same worksheet and if u wanna work on it together than u should add my discord: kuispe#1715

Answer:

I got you :)

Step-by-step explanation:

All angles of a triangle add up to 180 degrees so you can make the equation

3x-2+4x+9+3x-9=180  this equation will help you find x

I used the equation to find out that x=18.2 (i can explain this part further if you would like)

so now you know x=18.2 and all you have to do is plug in

m<H = 3 x 18.2 - 2 = 52.6

m<I =  4 x 18.2 + 9 = 81.8

M<J = 3 x 18.2 - 9 = 45.6

Hope this helps!  :)

Also to check work you can do 52.6+81.8+45.6= 180 :) you know its right because it equals 180 degrees at the end  

Answer:

2

Step-by-step explanation:

Answer:

D. the product of x and a factor not depending on x

Step-by-step explanation:

The equation for the given expression is:

[tex]x (2y+7z)^{2}[/tex]

According to the expression, there are two factors:

the first factor is x, and

the second factor is [tex](2y+7z)^{2}[/tex]

Since, the second factor do not contain x, therefore it is independent of x.

Hence, the expression for the given equation will be the product of x and a factor not depending on x.

Answer:

j = k - h/-7

Step-by-step explanation:

you make j all by itself

Answer: 138

Step-by-step explanation:

Answer:

Conner should get 2 $ back

Step-by-step explanation:

conner should get 2$ back

Hey there!

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Answer:

El decimal siempre va a la izquierda.

Step-by-step explanation:

Mueve el decimal el número de veces que el exponente es. Por ejemplo: 5.3x10^-2. En el 5.3 vas a mover el decimal 2 veces a la izquierda.

0.053

Utilizando el teorema, veremos que la altura de la torre es 7 metros.

El teorema de Tales nos dice que para triangulos similares, la razon entre los catetos debe ser igual.

Esto significa que la razon entre la altura y el largo de la sombra de un objeto debe ser una constante.

Sabemos que Kevin tiene una estatura de 1.75m y proyecta una sombra de 3.5m

El cociente es:

3.5m/1.75m = 2

Es decir, la sombra tiene una longitud de dos veces la altura.

Entonces si la sombra de la torre es de 14m y la altura es h, tendremos:

14m/h = 2

h = 14m/2 = 7m

La altura de la torre es de 7 metros.

Sí quieres aprender más sobre triangulos rectangulos, puedes leer:

https://brainly.com/question/25839532