A polygon has 35 diagonals. How many sides does it have?

Answers

Answer 1

Answer: $d=35\n d=(n(n-3))/(2)\n d=(n(n-3))/(2)\n35=(n(n-3))/(2)\n 70=n^2-3n\n n^2-3n-70=0\n n^2-10n+7n-70=0\n n(n-10)+7(n-10)=0\n (n+7)(n-10)=0\n n=-7 \vee n=10\n\n n=10$

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What is the value of SZT?

Answers

Answer:

$\boxed{m \angle SZT = 121 \degree }$

Given:

$m \angle RZT = 137 \degree \n m\angle RZS = 56 \degree$

Step-by-step explanation:

$= > m \angle RZT = m\angle RZS + m \angle SZT \n \n = >157 \degree = 36 \degree+ m \angle SZT \n \n = > 157 \degree - 36 \degree = m \angle SZT \n \n = > 121 \degree = m \angle SZT \n \n = > m \angle SZT = 121 \degree$

1. Which expressions are completely factored?Select each correct answer.

24a^4+18=6(4a^4+3)

12a^3+8a=4(3a^3+2a)

16a^5−20a^3=4a^3(4a^2−5)

30a^6−24a^2=3a^2(10a^4−8)

Answers

All but B, as on B an a can be factored out

A restaurant bill before tax is $15.50 if the sales tax is 8% and a 15% tip is added what is the total cost of the meal

Answers

Answer:

$19.07 total cost of dinner

Step-by-step explanation:

15.50 * 8%= 1.24

15.50 * 15%= 2.33

Add the cost of dinner plus tax plus tip to get the answer: $19.07

Which is greater 8 quarts or 16 pints?

Answers

They're equal because 1 quart = 2 pints.

Help with this question? I got half of it, but can't seem to get the other half. Please explain how you got your answer. Thanks!1. The equation of a plane in space is x + 3y + 2z = 6.
a.) Accurately sketch the plane on the set of axes, showing all your calculations below.
b.) The three planes of the axes and the plane you have sketched create a triangular pyramid. Find the volume of this pyramid, showing the formula you are using and all
calculations below.

My Answer:
a. I started off by finding my x-intercept. To find my x-intercept I substituted y and z with 0. So: x + 3(0) + 2(0) = 6. After multiplying and adding, I end up with x = 6. So my x-intercept is (6, 0, 0,). T find my y-intercept I substituted x and z with 0. So: 0 + 3y + 2(0) = 6. After multiplying and adding, we come up with 3y = 6. Now we divide each side by 3 to get y = 2. So my y-intercept is (0, 2, 0). To find my z-intercept, I substituted x and y with 0. So, 0 + 3(0) + 2z = 6. After multiplying and adding, I get 2z = 6. Now I divide each side by 2 to get z = 3. So my z-intercpet is (0, 0, 3). After I plotted the points and connected them, they formed a triangular pyramid.

So thats how much i got. I cant seem to figure out how to get the volume. please help.

Answers

Answer:

Volume of the pyramid = 6 cubic units

Step-by-step explanation:

The volume of a triangular pyramid is: V = (1/3)*A*H

where A is the area of the triangle base, and H is the height of the pyramid.

Taking the triangle formed in the x-y plane as the base, its area is computed as follows:

A = (1/2)*6*2 = 6 square units

where 6 and 2 are the measure of the two perpendicular sides of the triangle. This is taken from the x-intercept point (6, 0, 0) and y-intercept point (0, 2, 0).

The height of the pyramid is then the measure of the z-intercept point (0, 0, 3), that is, 3. Replacing in volume formula:

V = (1/3)*A*H

V = (1/3)*6*3

V = 6 cubic units

X - Intercept
    x + 3y + 2z = 6
x + 3(0) + 2(0) = 6
      x + 0 + 0 = 6
      x + 0 = 6
   - 0 - 0
      x = 6
X - Intercept: (6, 0, 0)

Y - Intercept
x + 3y + 2z = 6
0 + 3y + 2(0) = 6
    0 + 3y + 0 = 6
    0 + 0 + 3y = 6
      0 + 3y = 6
      - 0    - 0
      3y = 6
   3    3
      y = 2
Y - Intercept: (0, 2, 0)

Z - Intercept
x + 3y + 2z = 6
0 + 3(0) 2z = 6
0 + 0 + 2z = 6
      0 + 2z = 6
      - 0    - 0
      2z = 6
   2    2
      z = 3
Z - Intercept: (0, 0, 3)

Volume of the X - Intercept, Y - Intercept, and Z - Intercept
V = ¹/₃(¹/₂lwh)
V = ¹/₃(¹/₂(6)(2)(3))
V = ¹/₃(¹/₂(12)(3))
V = ¹/₃(¹/₂(36))
V = ¹/₃(18)
V = 6 u³

Graph the functions and approximate an x-value in which the exponential function surpasses the polynomial function. f(x) = 4x
g(x) = 4x2

The 2 in the 2nd equation is supposed to be an exponent btw