Please answer this question picture shown !!

Mathematics

1 answer:

Naddik [55]3 years ago

4 0

The answer is choice D because the expression 6x^3+x^2-3 is the same as 6x^3+1x^2+0x+(-3). Notice the coefficients are 6, 1, 0, -3

The expression x-7 is in the form x-k where k = 7. This is the test root which is placed outside of the synthetic division bar as shown in choice D.

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1. M is the midpoint of LN and O is the midpoint of NP.

Reptile [31]

1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation
MO= (1/2) LP

If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be:
2x+6= (1/2)( 8x-20)
2x+6= 4x-10
2x-4x= -10 - 6
-2x= -16
x=8

2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2

Then, the answer would be:
A.F= 1/(1+2) * AC
A.F= 1/3 * 12= 4

FC= 2/(1+2) * AC
FC= 2/3 * 12= 8

3. Since
∠BAD=∠DAC
∠ABD=∠ACD
AD=AD
The triangle ABD and ACD are similar. You can get this equation
BD=DC
x+8= 3x+12
x-3x= 12-8
-2x=4
x=-2

DC=3x+12= 3(-2) +12= 6

4. Orthocenter made by intersection of triangle altitude
A
BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be:
y=-x +a
0= 1+a
a=-1
y=-x-1
B
AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be:
y=1/3x+a
-1=1/3(4)+a
a=-7/3
y=1/3x - 7/3

C
BC lines slope would be (-1)-(-1)/4 = 0/4.
The line would be
0=x+a
a=-1
0=x-1
x=1

y=-x-1 = 1/3x-7/3
-x-(1/3x)=-7/3 +1
-4/3x= -4/3
x=1

y=-x-1
y=-1-1= -2
The orthocenter would be (1,-2)

5.
a. Circumcenter: the intersection of perpendicular bisector lines<span>
b. Incenter: the intersection of bisector lines
c. Centroid: </span>the intersection of median lines<span>
d. Orthocenter: </span>the intersection of altitude lines

5 0

3 years ago

See the picture below

mart [117]

Answer:

a) 301.59 cubic centimeters

b) 235.87 square centimeters

Step-by-step explanation:

Volume of ice cream cone is volume of hemisphere PLUS volume of cone.

Volume of Hemisphere = $\frac{\frac{4}{3}\pi r^3}{2}$

radius is given as 4, so,

Volume of Hemisphere = $\frac{\frac{4}{3}\pi r^3}{2}\\=\frac{\frac{4}{3}\pi (4)^3}{2}\\=134.04$

Now, Volume of Cone = $\frac{1}{3}\pi r^2 h$

Where radius is 4 and height is 10, so,

Volume of Cone = $\frac{1}{3}\pi r^2 h\\=\frac{1}{3}\pi (4)^2 (10)\\=167.55$

Volume of Ice Cream Cone = 134.04 + 167.55 = 301.59 cubic centimeters

Surface area of ice cream cone is surface area of hemisphere PLUS surface area of cone.

Surface Area of Hemisphere = $2\pi r^2\\=2\pi (4)^2\\=100.53$

Surface Area of Cone = $\pi r^2+\pi rl$

We dont need to use the first part, $\pi r^2$ since it is "inside". We need to find l, slant height, by using pythagorean theorem on a triangle we can make (bottom right).