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2 years ago

how many numbers have this property: when you subtract 297 from it, you get the same number but in reverse.

Mathematics

1 answer:

jasenka [17]2 years ago

8 0

9514 1404 393

Answer:

Step-by-step explanation:

Consider the number with digits x, y, z. Its value will be 100z+10y+z. We want the same value when we reverse the digits after subtracting 297.

100x +10y +z -297 = 100z +10y +x

99x -99z = 297 . . . . . subtract 100z+10y+x-297

x -z = 3 . . . . . . . . . . . . divide by 99

The first digit of the number is 3 more than the last digit. There are 60 such numbers. The first digit may be 4..9, and the middle digit may be 0..9.

401, 502, 603, ..., 906; 411, 512, 613, ..., 916, ..., 491, 592, 693, ... 996

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Algebra 2A Help ! Tadakimasu ~

Ludmilka [50]

Function is p(x)=(x-4)^5(x^2-16)(x^2-5x+4)(x^3-64)

first factor into (x-r1)(x-r2)... form

p(x)=(x-4)^5(x-4)(x+4)(x-4)(x-1)(x-4)(x^2+4x+16)
group the like ones
p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)

multiplicity is how many times the root repeats in the function
for a root r₁, the root r₁ multiplicity 1 would be (x-r₁)^1, multility 2 would be (x-r₁)^2

so

p(x)=(x-4)^8(x+4)^1(x-1)^1(x^2+4x+16)
(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1
(x^2+4x+16) is not on the real plane, but the roots are -2+2i√3 and -2-2i√3, each multiplicity 1 (but don't count them because they aren't real

baseically

(x-4)^8 is the root 4, it has multiplicity 8
(x-(-4))^1 is the root -4 and has multiplicity 1
(x-1)^1 is the root 1 and has multiplity 1

7 0

3 years ago

The probability distribution for a random variable x is given in the table X: -5,-3,-2,0,2,3 Probability: .17,.13,.33,.16,.11,.1

Ivan

Answer:

0.6 probability that $-2 \leq x \leq 2$

Step-by-step explanation:

The probability distribution is given in the table.

Probability that x is between -2 and 2.

Between -2 and 2, inclusive, we have -2, 0 and 2. So

$P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2)$

From the table:

$P(X = -2) = 0.33, P(X = 0) = 0.16, P(X = 2) = 0.11$ . So

$P(-2 \leq x \leq 2) = P(X = -2) + P(X = 0) + P(X = 2) = 0.33 + 0.16 + 0.11 = 0.60$

0.6 probability that $-2 \leq x \leq 2$

4 0

2 years ago

If a median, an altitude, and an angle bisector are the same segment in a triangle, the triangle is scalene

statuscvo [17]

Never is the right answer .

3 0

3 years ago

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
b. Incenter: the intersection of bisector lines
c. Centroid: the intersection of median lines
d. Orthocenter: the intersection of altitude lines

5 0

2 years ago

Question 17 please help

kramer

$\sqrt{9x^2} / \sqrt{18y^2}$
after taking sqrt both side

3x/ $\sqrt{9*2y^2}$

3x/3y√2
x/√2y
multiply both denomenator and numerator by√2
√2x/2y

Answer is A

8 0

3 years ago