Hi,

lengths of the legs have a sum of 17 centimeters

Let x and (17-x) represent the lengths of the legs

hypotnuse of this right triqangle measures 13 centimeters

Applying the Pythagorean Theorem

x^2 + (17-x)^2 = 13cm^2

solving for x

x^2 + 17^2 - 34x + x^2 = 13^2

2x^2 -34x +120 = 0

x^2 -17x + 60 = 0

factoring

(x-12)(x-5)= 0

(x-12)=0 x = 12

(x-5)= 0 x = 5

the lengths of the legs are 12cm and 5cm

CHECKING our Answer

144 + 25 = 169

Hi,

Note: the standard slope-intercept form for an equation of a line y = mx + b 

where m is the slope and b the y-intercept.  

2x-3y=6  Solving for y to put into slope-intercept form

2x - 6 = 3y

y = (2/3)x - 2  

m = (2/3)

parallel lines have identical slopes.  Answer C would be the correct choice

Hi,

the sum of their ages is 55 years

Let x and (55-x) represent their ages now



cross multiply to solve for x

6(55-x) = 5x

6*55  -6x = 5x

6*55 = 11x

30 = x  Two suspects are 30 and 25 years old now.



Let y represent the number of years from now the ratio will be 8:7

(30+y)/(25+y) = 8/7  cross multiplying to solve for y

8(25+y) = 7(30+y)

8*25 + 8y = 7*30 + 7y

y = 210 - 200 = 10, the years from now the ratio will be 8:7

Hi,

f(x)=sqrt(x) + 1  Pt(0,1), Pt(4,3), Pt(9,4)on the graph of the function

Range (1, ) domain (0,)

Hi,

the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.

3x-6y=12  Solving for y to put into the slope-intercept form

3x - 12 = 6y

y = (3/6)x - 2  Or y = (1/2)x - 2    Pt(0,-2) and (4,0) points on the line

m = (1/2)  As y increases/decreases by 1, x increases/decreases by 2

Hi,

Determine the domain and range of the function and graph it

f(x)=(x-6)^2+5

the vertex form of a parabola,  where(h,k) is the vertex

vertex is Pt(6,5) Range (5, )Domain(, )Or all real numbers.

Hi,

Find all the solutions between 0 and 2pi to the equation

cos(2x)=sin(x)+1

 = 1 - 2sin^2

1 - 2sin^2(x) = sin (x) + 1

2sin^2(x) + sin (x) =0

sin(x)[2sin(x) + 1] = 0

sin(x)=0

x = 0, 

2sin(x) + 1 = 0

sin(x) = -1/2

x = 7/6 pi, 11/6 pi

(cos(x), sin(x))

Hi

 x-intercepts (to the nearest tenth) of the equation f(x)=-2x^2+4x+3

0 = -2x^2 + 4x + 3











x = 1 - 1.58 = -.58 = -.6

x = 1 + 1.58 = 2.58  = 2.6

x- Intercepts: Pt(-.6,0) and Pt(2.6,0)

Hi,

Let x represent the length of the shorter leg.

then the hypotenuse is (2x-3) and the other leg is (x+3)

Applying the Pythagorean Theorem***

x^2  + (x+3)^2 = (2x-3)^2

solving for x

x^2 + x^2 + 6x + 9 = 4x^2 -12x + 9

2x^2 - 18x = 0

2x(x-9)= 0

x = 0 Extraneious solution

x = 9, the length of the shorter leg. Other two sides are 12 & 15

CHECKING our Answer***

81 + 144 = 225

Hi,

bakes x cakes ... gives two of them away

Mrs Jones keeps (x-2) cakes

Hi

one leg of a right triangle is 12 cm longer than the other

Let x and (x+12cm) represent the lengths of the legs of this right triangle

A = (1/2)b*h

110cm^2 = (1/2)x(x+12cm)

220 = x^2 + 12x

0 = x^2 + 12 - 220

factoring

(x+22)(x-10)= 0 Note:SUM of the inner product(22x) and the outer product(-10x) = 12x

(x+22) = 0

x = -22 extraneous solution

(x-10)= 0

x = 10   10cm and 22cm are the lengths of the two legs

Letting c represent the length of the longer lefg & applying the Pythagorean Theorem

10^2 + 22^2 = c^2

584 = c^2  (discarding negative solution for length)

24.17cm  = c

Hi

D = r*t  Units are in a consistent form in the question

D = 350mph*3hr = 1050mi, the distance the plane travels in 3 hours

Hi

side of an equilateral triangle measures 10 inches

Let x represent the height. Applying the Pythagorean Theorem

5^2 + x^2 = 10^2

25 + x^2 = 100

x^2 = 75  Note: negative solution is extraneous for length

Hi

D = r*t  Note: all units of measure must be consistent.  45min = 3/4 hr

D = 80mph*(3/4)hr = 60mi

Hi

a)probability that an 18-year-old man selected at random is between 68 and 70 inches tall

 

 = .5  NORMSDIST(.5)  = .6915

= -.5  NORMSDIST(-.5) = .3085

P(-.5 < z > .5) = .6915 - .3085 = .3829  Or 39.29%



b)random sample of sixteen 18-year-old men is selected

test statistic = 

 z= 1/(2/4)  =  2  NORMSDIST(2)  = .6915 = .9773

 z = -1/(2/4)= -2  NORMSDIST(-2)  = .6915 = .0228

P(-2 < z > 2) = .9973 - .0228 = .9545  Or 95.45%

Hi

D = r*t

you take 10 minutes to walk from home to school at a rate of 264ft./min.

D = 264ft/min*10min = 2640ft, the distance to school for You

Your friend lives closer to school than you do.

D.   d < 2640ft would be the correct selection for your friend's distance

Hi,

m-7 ≥ -8  Adding 7 to both sides of the inequality

m ≥ -1

Hi

log 2 (x-1) - log 2 (x+3) = log 2 (1/x)

log 2 (x-1) - log 2 (x+3) - log 2 (1/x)=0



=0



2^0 = (x-1)/(x+3)(1/x)



1 = x(x-1)/(x+3)

(x+3) = x^2 -x

x^2 -2x - 3 = 0

(x-3)(x+1)= 0

(x-3)=0    x = 3

(x+1)= 0   x = -1 reject as a solution

Any solution that makes an argument (or base) zero or negative must be rejected.

log 2 ((-1)-1) - log 2 ((-1)+3) = log 2 (1/(-1))

Hi,

Find the center and radius of the circle

The standard equation of a circle with center C(h,k) and radius r is :



x^2+y^2-6x+2y+6=0

(x-3)^2 + (y+1)^2 -9 -1 + 6 = 0

(x-3)^2 + (y+1)^2 = 4

(x-3)^2 + (y+1)^2 = 2^2

Center is Pt(3,-1) r = 2

Hi,

Solving

3x^2=4x-1

3x^2 - 4x + 1 = 0

factoring

(3x -1)(x -1)=0 Note:SUM of the inner product(-1*x) and the outer product(-3x) = -4x

(3x -1)=0

x = 1/3

(x -1)=0

x = 1

Hi,

The First and Fourth terms of a geometric sequence are 5 and 135

Note: for a geometric series: 





135 = 5*r^3

27 = r^3

3 = r

Hi,

Let x represent the number of quarters, then (86-x) would be the number of dimes

Question states

25x + 10(86-x) = 1460 cents

solving for x

25x + 860 - 10x = 1460

15x = 600

x = 40, the number of quarters.  46 dimes  (86-40)

CHECKING our Answer

25*40 + 10*46 = 1000 + 460 = 1460 cents or $14.60

Hi,

Let x, (x+1) and (x+2) represent the three consecutive integers

Write as we Read***

4[x + (x+1) + (x+2)]=2(x+1)(x+2)

solving for s

4x + 4x + 4 + 4x + 8 = 2[x^2 + 3x + 2]

12x + 12 = 2x^2 + 6x + 4

2x^2 -6x - 8 = 0

x^2 - 3x  -4 = 0

(x-4)(x+1) = 0

(x-4)=0  x = 4 three consecutive integers are 4,5,6

(x+1)=0  x = -1 three consecutive integers are -1,0,1

CHECKING our Answers***

4 * 15 = 2*30 = 60

4 * 0 = 2 * 0*1 = 0

Hi,

Let x represent how high is the top of the ladder

Applying the Pythagorean Theorem

5^2 + x^2 = 10^2

25 + x^2 = 100

x^2 = 75

 (positive solution only appropriate here)

x = 11.18 ft, how high the top of the ladder is

Hi,

Let x represent the number

Write as we Read***

(x + 10)*4 = 22

solving for x

4x + 40 = 22

4x = -18

x = -18/4  Or -9/2

CHECKING our Answer***

Hi

Note: the vertex form of a parabola,  where(h,k) is the vertex

f(x)=x^2-4x+3 Or f(x)= (x-2)^2 -1 in vertex form: x-intercepts (3,0)&(1,0)

vertex Pt(2,-1), axis of symmetry x = 2, (0,3) the y-intercept



f(x) = (x+1)^2-4  x-intercepts (1,0)&(-3,0)

vertex Pt(-1,-4), axis of symmetry x = -1, (0,-3) the y-intercept

Hi

Let x represent time in minutes it takes to fill the tank together

Per minute is the Equalizer

1/45 + 1/55 = 1/x  Mulitplying each term by 45*55x so as all denominators = 1

55x + 45x = 45*55

100x = 45*55

x = 45*55/100

x = 27.75 min, time in minutes it takes to fill the tank together

Hi

Each of the 3 north face trails has two options on the south face going down

3*2 = 6

6 is the total number of different routes possible going up the north face and down the south face

Hi

(385-365)/(100/(sqrt 25)) = 20/20 = 1 Note: 

Z table or NORMSDIST(1)= .8413

1 - .8413 = .1587 Or 15.87% is the probability that the sample mean concentration will be above 385 parts per million. 

Hi

c=2x+20

Can only assume that x is the number of units and c is the cost of producing them.

 (a)$430  

$430 = 2x + 20

$410 = 2x

205 = x, the number of units costing $430  (205,430)

(b)$700  c = $700

$700 = 2x + 20

$680 = 2x

340 = x, the number of units costing $700 (340,700)

(c)$1,400  c =$1400

$1400 = 2x + 20

$1380 = 2x

690 = x the number of units costing $1400 (690,1400)