3 sides of the triangle are consecutive odd numbers. What is the smallest possible perimeter of the triangle ?

Answer:

f(g(x)) = [tex]\sqrt{8x-22}[/tex]

Step-by-step explanation:

Substitute x = g(x) into f(x), that is

f(g(x))

= f(8x - 13)

= [tex]\sqrt{8x-13-9}[/tex]

= [tex]\sqrt{8x-22}[/tex]

Answer:

A. linear, because it's growing the same amount each growing season

Step-by-step explanation:

Answer:

Step-by-step explanation: the answer is linear because it goes up by a constant every year

Let Length of each Plan A workout be [tex] a[/tex]

and Length of each Plan B workout be $b$

on Wednesday,

$5a+3b=7$

$2a+12b=19$

multiply equation one by $4$ and subtract equation two from it

to get,

$18a=9$ or $a=\frac12$

substitute $a$ in eq 2. to get $b$, $12b=18\implies b=\frac32$

Answer: 7√2

Step-by-step explanation: To simplify a square root where the number inside the radical is not a perfect square like the square root of 98, we start by making a factor tree for the number inside.

98 factors as 2 · 49 and if you know your perfect squares,

you should be able to recognize 49 as 7 · 7.

What we are looking for in our factor tree

are pairs of factors that are the same.

If a factor pairs up, it will come out of the radical.

If a factor does not pair up, then it stays inside the radical.

So here, since our 7's pair up, a 7 will come out of the radical.

Since the 2 does not pair up, it stays inside the radical.

So our answer is 7√2.

Answer:

x = 69.4

Step-by-step explanation:

law of sines

sine x/4 = sine 55/3.5

x = ( sine(55) * 4 ) / 3.5

x = inv sine (0.936)

x = 69.4

Answer:

(a) ∠EFH =  68°

(b) ∠EGF = 21°

Step-by-step explanation:

(a) The given parameters are;

The diameter of the circle = Segment [tex]\overline{EG}[/tex]

Arc [tex]m\widehat{FG}[/tex] = 138°

∠GFH = 22°

∠ EFG = (Angle subtended by the diameter EG at the center)

Arc mEG = 180° (Arc subtended by the diameter of a circle = 180°)

∠ EFG is subtended by the diameter EG at the center

∴ ∠ EFG = 90° (Angle at the center = 2 times angle at the circumference)

∠EFG = ∠EFH + ∠GFH  (Angle addition postulate)

∴ ∠EFH = ∠EFG - ∠GFH = 90° - 22° = 68°

∠EFH =  68°

(b) ∠EGF

Arc GH = 44°

Arc mFE + Arc [tex]m\widehat{FG}[/tex] + Arc mEHG = 360 (Sum of angles at the center of a circle)

Arc mFE = 360 - ( Arc [tex]m\widehat{FG}[/tex] + Arc mEHG )

Arc mFE  =  360 - 180 - 138 = 42°

∠EGF = Arc mFE/2 (Angle at the center = 2 times angle at the circumference)

∠EGF = 42/2 = 21°

∠EGF = 21°

Answer:

F = -16

Step-by-step explanation:

F/4-5=-9

Add 5 to each side

F/4-5+5=-9+5

F/4=-4

Multiply each side by 4

F/4 *4=-4*4

F = -16

Answer:

$200,000 in bank A, $200,000 in bank B, $230,000 in bank C

Step-by-step explanation:

Meredith has $630,000

Limit per depositor, per bank, is $250,000

She needs to distribute her money between three Banks to guarantee that her money is insured.

A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C

It can be seen in A that her deposit per bank deposit didn't exceed the $250,000 limit in the three Banks.

B. $200,000 in bank A, $170,000 in bank B, $260,000 in bank C

Here, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C

C. $160,000 in bank A, $180,000 in bank B, $290,000 in bank C

Her deposit in bank C is $290,000 which exceeds the $250,000 limit. Therefore, no guarantee for insurance of her money in bank C

D. $160,000 in bank A, $200,000 in bank B, $270,000 in bank C

you

Also, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C

The way her money can be distributed between three Banks and guarantee insurance is

A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C.

That way, her deposit per bank is less than the $250,000 limit

Answer:

2x^2 +5x-12

Step-by-step explanation:

(2x - 3)(x + 4)

FOIL

first 2x*x = 2x^2

outer  2x*4 = 8x

inner  -3x

last -3*4 = -12

Add these together

2x^2 +8x-3x-12

Combine like terms

2x^2 +5x-12

Answer:

Step-by-step explanation:

[tex]3 \times 19 \times 14 + 18 \div 2 \\ PEDMAS \\ (3 \times 19 \times 14 )+ 9 \\ = 798 + 9 \\ [/tex]

[tex] = 807[/tex]

Answer:

408

Step-by-step explanation:

3x19= 57

57x14= 798

798 + 18= 816

816/ 2= 408

Answer:

the slope of the line x+y = 6 is -1.

Step-by-step explanation:

slope = - coefficient of x

----------------------

coefficient of y

slope = -1 /1

slope = -1

Answer:

A: -1

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The common ratio r of a geometric sequence is calculated as

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{3}[/tex] → C

Answer:

C)

Step-by-step explanation:

Geometric Sequence:

3, 4 , [tex]\frac{16}{3}[/tex]......

Common ratio = [tex]\frac{second term}{first term}[/tex]

  = [tex]\frac{4}{3}[/tex]

Answer:

(1 +1/34) to the power of 34

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

in the quadratic formula to only have one solution

[tex]b^{2} -4ac=0[/tex] for [tex]ax^2+bx+c=0[/tex]

so we have

[tex]ax^2+b=c[/tex]

[tex]ax^2+(b-c)=0[/tex]

if we insert in the formula we have

[tex]0^2-4(a)(b-c)=0\\\\-4ab+4ac=0\\\\4ac=4ab\\\\\frac{4ac}{4a} = \frac{4ab}{4a}\\\\c=b[/tex]

[tex]ax^2+b=c\\\\ax^2=b-b\\\\ax^2=0[/tex] since a≠0

[tex]\frac{ax^2}{a}=\frac{0}{a} \\\\x^2=0\\\\x=0[/tex]

Answer:

x = 12

Step-by-step explanation:

If Mary spent $45 altogether,

then she bought lunch for $9

so our equation now is

$45 = $9 + 3x

It is 3x because he bought 3 shirts and we used x because we didnt

now how much the price of those shirts were

$45 = $9 +3x

$45 - $9 = 3x

$45 - $9 = $36

$36 = 3x

$36 / 3 = 12

x = 12

Please mark this answer as the brainliest

Answer:

C.

Step-by-step explanation:

The transformation f(x) ---> a f(x) stretches the graph  of f(x) vertically by a factor a.

The point (1, 1) on f(x) transforms to  (1,9) on g(x).

This is a vertical transformation  of factor 9, so g(x)  = 9f(x)

= 9x^2  or (3x)^2.

Answer:

  x = {π/4, 7π/6, 5π/4, 11π/6} +2kπ . . . for any integer k

Step-by-step explanation:

  [tex]\dfrac{\sin^3{x}}{1+\cos{x}}+\dfrac{\cos^3{x}}{1+\sin{x}}=\cos{2x}+2\cos{x}-1\\\\\dfrac{\sin{x}(1-\cos^2{x})}{1+\cos{x}}+\dfrac{\cos{x}(1-\sin^2{x})}{1+\sin{x}}=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}(1-\cos{x})+\cos{x}(1-\sin{x})=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}+\cos{x}-2\sin{x}\cos{x}=2\cos{x}-2\sin^2{x}\qquad\text{use $1=s^2+c^2$}\\\\\sin{x}+2\sin^2{x}-\cos{x}-2\sin{x}\cos{x}=0\\\\\sin{x}(1+2\sin{x})-\cos{x}(1+2\sin{x})=0\\\\(\sin{x}-\cos{x})(1+2\sin{x})=0[/tex]

This will have solutions where the factors are zero.

sin(x) -cos(x) = 0

Dividing by cos(x), we have ...

  tan(x) -1 = 0

  x = arctan(1) = π/4, 5π/4

1 +2sin(x) = 0

  sin(x) = -1/2

  x = arcsin(-1/2) = 7π/6, 11π/6

The four solutions in the interval [0, 2π] are x = {π/4, 7π/6, 5π/4, 11π/6}. Solutions repeat every 2π radians.

_____

Additional comment

We have made use of the factoring of the difference of squares:

  (1 -a^2) = (1 -a)(1 +a)

and we have made use of the cosine double angle identity:

  cos(2x) = cos(x)^2 -sin(x)^2

The "Pythagorean" identity for sine and cosine was used several times:

  1 = sin(x)^2 +cos(x)^2

Answer:

.6239 as a fraction is 6239/10000.

Answer:

The slope is

Step-by-step explanation:

To find the slope of AB we use the formula

Where

m is the slope and

(x1 , y1) and (x2 , y2) are the points

The slope of AB

A (-3, 12), B (-11, -16) is

We have the final answer as

Hope this helps you

Answer:

y=3

Step-by-step explanation:

7y-(5y+4)=10

7y-5y+4=10

         -4    -4

7y-5y=6

2y=6

÷2   ÷2

y=3

Answer:answer=A

Step-by-step explanation: 3×3×3×2×2=72

Answer:

YUP THEY RIGHT

Step-by-step explanation:

Answer:

D. Terms that have identical variable parts

Step-by-step explanation:

Like terms refers to terms that have identical variable parts.

For example:

Given the expression

2xy + z + x + 3y - 5z + 4y - xy + 3x

The like terms in the expression are:

2xy - xy= xy

z - 5z= -4z

x + 3x= 4x

3y + 4y=7y

The new expression will be

xy - 4z + 4x + 7y

Answer:

m<C = 102°

Step-by-step explanation:

Step 1: find measure of arc BC.

According to the Inscribed angle theorem of a circle, an inscribed angle is half the measure of the arc it intercepts.

m<D intercepts arc ABC

thus, 80° = ½(120+BC)

Solve for BC. Multiply both sides by 2

80*2 = 120 + BC

160 = 120 + BC

BC = 160 - 120 = 40°

Step 2: Find m < A

According to the Inscribed angle theorem, m < A = ½ of arc BCD = ½(40 + 116)

m < A = 78°

Step 3: find m < C

m < A + m < C = 180 (opposite angles of an inscribed quadrilateral are supplementary)

m < C = 180 - 78 = 102°

Answer: It is a Rotation Angle 90 Degrees clockwise about the point (3,4)

Step-by-step explanation:

Mark the point (3,4) with your finger and turn your phone once to the right Your old shape is where your new shape your be now. That’s rotation.

Answer:

A. 5

Step-by-step explanation:

Based on the secant and tangent theorem, (4 + x)*4 = 6²

We can solve for x using the equation which describes the relationship between secant and tangents.

Thus,

[tex] (4 + x)*4 = 6^2 [/tex]

[tex] 4*4 + x*4 = 36 [/tex]

[tex] 16 + 4x = 36 [/tex]

Subtract 16 from both sides

[tex] 4x = 36 - 16 [/tex]

[tex] 4x = 20 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{20}{4} [/tex]

[tex] x = 5 [/tex]

Answer:

A.) median; 1.5

Step-by-step explanation:

Hello!

The median is the number that is in the middle when the numbers are listed from least to greatest

0, 0, 1, 1, 2, 2, 2, 14

We can take one from both sides till there are one or two numbers left

0, 1, 1, 2, 2, 2

1, 1, 2, 2

1, 2

If there are two numbers left we add them then divide by 2 to get the median

1 + 2 = 3

3 / 2 = 1.5

The answer is A.) median; 1.5

Hope this helps!

Answer:5

Step-by-step explanation:30/600×100

Answer:

Step-by-step explanation:

[tex]\frac{30}{600} \times 100\\\\= \frac{3000}{600}\\ \\= 5\%[/tex]

Answer:

$178.3

Step-by-step explanation:

The value of a car is $20,000

The car loses 10.7% of its value yearly

Since there are 12 months in a year then 10.7% can be represented as

10.7%/12

= 0.8916%

Therefore the approximate monthly decrease in value can be calculated as follows

= $20,000×0.8916/100

= $20,000×0.008916

= $178.3

Hence the approximate monthly decrease in value is $178.3

Answer:

Option (2)

Step-by-step explanation:

In the given circle,

[tex]m(\widehat{CBD})+m(\widehat{CED})[/tex] = 360°

Therefore, 212° + [tex]m(\widehat{CED})[/tex] = 360°

[tex]m(\widehat{CED})=360-212[/tex]

               = 148°

Tangent - chord theorem states,

"Angle between a chord and tangent measure the half of the angle measure of the intercepted minor arc."

m∠ACD = [tex]\frac{1}{2}(\widehat{CED})[/tex]

              = [tex]\frac{1}{2}(148)[/tex]  

              = 74°

Therefore, measure of ∠ACD is half the measure of arc CD or 74°.

Option (2) will be the correct option.