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Elis [28]
3 years ago
9

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!

Mathematics
2 answers:
AlladinOne [14]3 years ago
7 0
<u>X - Intercept</u>
    x + 3y + 2z = 6
x + 3(0) + 2(0) = 6
        x + 0 + 0 = 6
              x + 0 = 6
              <u>   - 0  - 0</u>
                    x = 6
X - Intercept: (6, 0, 0)

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

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

<u>Volume of the X - Intercept, Y - Intercept, and Z - Intercept</u>
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
KIM [24]3 years ago
5 0

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

You might be interested in
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f
GalinKa [24]

Answer:

\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in \mathbb{R}.

\\f(x)=(x^2+16)(x^2-2x-15)

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}

And we can write in \mathbb{C}

f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0
3 years ago
staci has seven more cats than Talyor. write an expression that illustrates how many cats staci has. use x to represent the numb
belka [17]
X = 7 + staci  since 7 more cats added to x is stacis amount
7 0
2 years ago
Read 2 more answers
URGENT HELP NEED!!! I WILL REWARD LOTS OF POINTS FOR THIS QUESTION!!! ANY IRRALEVENT OR SILLY QUESTION WILL BE INSTANTLY REPORTE
Ipatiy [6.2K]

Let the points be A,B,C

  • A(0,0)
  • B(24,16)
  • C(8,20)

#A

\\ \bull\sf\leadsto AB=\sqrt{(24-0)^2+(16-0)^2}=\sqrt{24^2-16^2}=\sqrt{576-256}=\sqrt{320}=17.4units(leg3)

\\ \bull\sf\leadsto AC=\sqrt{(8-0)^2+(20-0)^2}=\sqrt{8^2+20^2}=\sqrt{64+400}=\sqrt{464}=21.4units(leg1)

\\ \bull\sf\leadsto BC=\sqrt{(24-8)^2+(26-20)^2}=\sqrt{16^2+(-4)^2}=\sqrt{256+16}=\sqrt{272}=16.4units(leg2)

#B

We have to find perimeter

\\ \bull\sf\leadsto Perimeter=AB+AC+BC

\\ \bull\sf\leadsto Periemter=17.4+16.4+21.4

\\ \bull\sf\leadsto Perimeter=55.2units

#C

The length of leg3=17.4units

5 0
3 years ago
Read 2 more answers
Help, I need somebody to help me out with this question.
Rama09 [41]
The first one is 4•7 I believe
4 0
3 years ago
Find the solution of 4 times the square root of the quantity of x plus 2 equals negative 16, and determine if it is an extraneou
Sonbull [250]
Your wording amounts to the equation
4*sqrt(x)+2=-16
4*sqrt(x)=-18
sqrt(x)=-9
but square roots are nonnegative so no solution exists.

5 0
3 years ago
Read 2 more answers
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