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Since thee are 7 different triangles, I will need more information please. Is there a relationship between the angles, between the sides? Is it a right or not?

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Let's start with the base. assume I can only use integers:
base = 2, leg = 31, 31
base = 4, leg = 30, 30
base = 6, leg = 29, 29
base = 8, leg = 28, 28
base = 10, leg = 27, 27
base = 12, leg = 26, 26
base = 14, leg = 25, 25
base = 16, leg = 24, 24
base = 18, leg = 23, 23
base = 20, leg = 22, 22
base = 22, leg = 21, 21
base = 24, leg = 20, 20
base = 26, leg = 19, 19
base = 28, leg = 18, 18
base = 30, leg = 17, 17
There are 15 options.

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You want both girls, so of the 8 boys you choose 0 boys and of the 6 girls, you choose 2 girls. There are 14 kids and you are choosing 2. So,

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Here is the original problem.
f(x)=log [(x-2)/(x-1)]
The domain of any log >=0
Step 1 -set (x-2) / (x-1) >= 0
First notice that if x = 1, our fraction is undefined.
* X cannot = 1
step 2 - multiply both sides by (x-1) to get
(x-2) >= 0
solving for x, we see
** x cannot = 2.
So it appears that x cannot equal 1 or 2.

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Let's take this part by part:
1. Express as a single logarithm and if possible, simplify.

Step 1 - use the power rule and bring the 2 up to the exponent:

step 2 - rewrite the square root a 1/2 power and cancel with the 2.

step 3 - since the bases are the same and we are subtracting, we can combine and make this division as

step 4 - we can reduce by x; assuming x is not 0 as

--
2. Choose the expression or equation that is equivalent to the one given
Log_x(29) = 5
a. 29^x=5
b. X^29=5
c. 5^x=29
d. X^5=29
My answer is "d" is that right?
[D] is correct.
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3. Express as a sum, difference, and product of logarithms, without using exponents:
/
step 1 - since 5y^8 is the big exponent, that comes out front using power rule

step 2 - since we are multiplying 2 and x, we can split it using addition as

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There is only 1 way to get 2,3,4 in that order. The total number of ways for the 3 balls is 9*8*7 = 504.
So, success = 1, total = 504, fail = 503.
odds = success / failure, so 1:503.

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Here are the two equations:
(i) 1x - 5y = -47
(ii) -4x - 5y = -37
multiply (i) by -1 to get
(iii) -1x + 5y = +47
(ii) -4x - 5y = -37
add down and find x.
(iv) -5x = 10
x = -2
solve for y.
y = 9.
(-2,9)

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This is a mixture problem. Here is the table:
nickel . . . . . % . . . . .mg . . . . . %g
45 . . . . . . .45 . . . . .g . . . . . 45g
100 . . . . . . 100 . . . . 6 . . . . . 600
Mixture . . .. .78 . . . . g + 6 . . . .78g + 468
Now, in the right hand column,
45g + 600 = 78g + 468
33g = 132
g = 4.
4 mg of metal at 45%.

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If you are given a value called ,
-a = the opposite of what you were given.
|a| is always the positive number a.
hope that helps.

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Parabola have the equation:

where h,k is the vertex. We are given (0,3) as well as (-4, -45). Putting all of this in, we can find a as:




The equation is

or simply

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Area of circle has the formula:

Your area was given as 225pi, so we have

divide by pi to get

take a square root and we get

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Step 1 solve for y;
y = -x^2 + 6x + 1
step 2: complete the square on the right side as:
y = -(x^2 -6x + ___ ) + 1 + ___
y = -(x^2 - 6x + (-3)^2) + 1 + 9
y = -(x-3)^2 + 10.
Now you are ready to graph

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Standard form requires two things: (1) all variable on the same side and (2) no fractions.
--
2y=-2x+6
Here we need variables on the same side so, we get
2x + 2y = 6.
Since there are no fractions, we are done.
--
y=3/4x+1/2
Here we have fractions. Multiply by 4, the common denominator. We get
4y = 3x + 2
Now put all variables on the same side. We get
-3x + 4y = 2.
Some teachers are picky about this and require x to be positive.

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This is a quadratic opening down with vertex at(-1,-2)

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I assume x is in the numerator. This is a linear function with negative slope and a positive y-intercept.

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The "if" part is the hypothesis, so we say:
3x - 7 = -4.

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Here is the original problem:

with coordinate (2,1).
substitute X and Y into the equation to get



So, the equation should be:
x + 3Y = 5.
Hope that is what you were looking for.

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Complementary angles add to 180 degrees, or
X + Y = 180.
If one angle is 19, then the other is 180 - 19 or 161 degrees.

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Hope this idea works for you. Draw a diagram that meets the criteria. Notice it appears to be a trapezoid.
STATEMENT 1: angle AXY congruent to angle AYX
REASON 1: given
STATEMENT 2: angle AXC congruent to angle AYB
REASON 2: given
STATEMENT 3: angle C congruent angle B.
REASON 3: if the top leg angles of a trapezoid are congruent then there base angles are congruent.
STATEMENT 4: triangle AXC congruent to triangle AYB
REASON 4: AAS postulate
STATEMENT 5: segment BY congruent segment CX
REASON 5: CPCTC

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Let A = paint brush and E = pencils.
E = 6A
A + E = 63
By substitution, we get
a + 6A = 63
7A = 63
A = 9
E = 54
9 paint brushes and 54 pencils.

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Let X and Y be the numbers.
X = Y + 5
5Y = 4X.
By substitution, we get
5Y = 4(Y+5)
5Y = 4Y + 20
Y = 20.
X = 25.

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First thing is to write everything in descending order and not to skip any terms: we have:

we solve X + 6 = 0 for x to get x = 6. Now we are ready.
6.// . 1 . . -6 . . 1 . . -6
. . . . . . 6 . . .0 . . 6
______________________________
. . . 1. . 0 . . . 1 . . 0.
So, if all of this works correctly, you will see
X^2 + 1 with no remainder.

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A horizontal line has equation:
Y = 0x + b.
The coordinate was (6,18)
18 + 6*0 + b
18 = b
So, we just have Y = 18.

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This is a proportion problem:
building ht / building shadow = hoop ht. / hoop shadow. We can see this better as:
(i) =
we are given building_ht = 90
hoop_ht = 10
hoop_shadow = 7.
We need to find building_shadow = B.
place this information into (i) to get
(ii) =
cross multiply to get
(iii)
B = building_shadow = 63 ft.
--
Now if building_ ht = 180, we get
(iii) =
cross multiply to get
(iv)
B = building_shadow = 126 ft.
--
We can see that double the ht means double the shadow.

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First we have a profit function as:

Second, we have D >= 80 and S >= 100. graph those on a coordinate system where D is x-axis and S is y-axis.
Third, we have D + S <= 200. Graph that on a coordinate system. Notice we get a "feasible region" which looks like a small triangle. We want the coordinates of the three verticies. They are: (80, 100) ; (80,120) ; (100,100).
Put these into the profit function and we get,
- -> P = 5000
- -> P = 5600
- -> P = 5500.
WE can see max profit at (80, 120).
we need to produce 80 deluxe and 120 standard.

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We have the original equation as
(i) 2y x 4x + 40 = 180
subtract 40 to get
8xy = 140
(ii) xy = 17.5 = 35/2
(iii) 2x = 35y
(iv) 4x = 70y
substituting back into (i) and subtracting 40, we get
(v) 2y*70y = 140
(vi) 140y^2 = 140.
Y = +-1.
If y = 1, then x = 17.5
If y = -1, then x = -17.5
They both work in the original equation.

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I an mot sure what you are saying here: are these coordinates, are the numbers in the right order? more information please.

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Here are the equations:
(i) 10x + 3y = 8
(ii) 2x + y = 2
Solve (ii) for y. It is easiest.
(i) 10x + 3y = 8
(iii) y = -2x + 2
substitute (iii) into (i) to get
10x + 3(-2x+2) = 8
10x - 6x + 6 = 8
4X = 2
X = 1/2
find Y.
Y = 1.
(1/2, 1)

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The difference between two numbers is 13 translates to
X - Y = 13
Two times the larger is 17 less than 3 times the smaller translates to
2X = 3Y - 17.
We can solve by substitution and get
2(y+13) = 3y - 17.
2y + 26 = 3y - 17
43 = y
x = 56
(56, 43)

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TO solve using elimination, we need all variables on the same side and lined up.
(i) 4s - 5t = 18
(ii) 6s + 10t = -8
multiply (i) by 2. We get
(iii) 8s - 10t = 36
(ii) 6s + 10t = -8
add down and solve for s.
(iv) 14s = 28
s = 2.
Find t.
t = -2
(2, -2)

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STATEMENT 1: circle with center at C.
REASON 1: given
STATEMENT 2: OC PERP. AB
REASON 2: given
STATEMENT 3: angle OCA congruent angle OCB
REASON 3: definition of perpendicular lines
STATEMENT 4: OC congruent OC
REASON 4: reflexive property of equality
STATEMENT 5: OA congruent OB
REASON 5: all radii of the same circle are congruent.
STATEMENT 6: triangle OCA congruent triangle OCB
REASON 6: HL postulate
STATEMENT 7: AC congruent BC
REASON 7: CPCTC
STATEMENT 8: OC bisect AB
REASON 8: definition of segment bisector.