If f(x) =x/4 - 3 and g(x) = 4x2 + 2x - 4, find (f +g)(x).
A. x2-12
B. 4x2 +Zx-7
C. 4x2+2x+1
D. 4x2+x-7

Answer:

PT = 16.3 units

Step-by-step explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]

[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]

[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]

[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]

[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]

PT = [tex]\frac{49}{3}[/tex]

PT = 16.3 units

A standard die has numbers = 1,2,3,4,5 and 6

Total outcomes = 6

P = Number of outcomes/Total Outcomes

Even and less than 4 = 1,2,3,4 and 6

P = 5/6

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The cost for one batch of fried rice will be $4.62.

Since the rice is bought at $0.71 a pound and one batch of fried rice requires 6.5 pounds of rice, then the cost of one batch of rice will be:

= $0.71 × 6.5

= $4.615

= $4.62 approximately.

In conclusion, the cost for one batch of fried rice will be $4.62.

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Answer:

the cost of the tire=341.4$

Answer:

Graph A

Step-by-step explanation:

A directly proportional relationship must create a straight line that goes through the origin (0,0) ( note that the slope can be negative or positive in a proportional relationship. )

All graphs show a straight line going through the origin except Graph A.

Graph A shows a straight line however that line does not go through the origin therefore it is not a proportional relationship

a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9

b) The height of the shorts at t =  10 minute is approximately 6 meters

The above answers were arrived at as follows

a) The general form of a sinusoidal equation is presented as follows;

y = A·sin(B(t - h)) + k

Where;

A = The amplitude of the graph of the function

The period, T = 2·π/B

h = The horizontal shift

k = The vertical shift

The maximum height of the blade = 16 meters

The minimum height of the blade  = 2 meters

The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s

Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s

Therefore;

B = 2·π/30 = π/15

B = π/15

When B·(t - h) = π/2, t = 10

Therefore;

(π/15)·(10 - h) = π/2

10 - h = 15/2

h = 10 - 15/2 = 2.5

The horizontal shift, h = 2.5

The amplitude, A = (Max - Min)/2

∴ A = (16 - 2)/2 = 7

A = 7

The vertical shift, k = Min - (-Amplitude)

∴ k = 2 - (-7) = 9

The vertical shift, k = 9 Up

Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to  get the following equation;

y = 7·sin(π/15·(t - 2.5)) + 9

b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;

y = 7·sin(π/15·(t - 2.5)) + 9

10 minutes =  600 seconds

When t = 10 minutes = 600 seconds

∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6

The height of the shorts at exactly t = 10 minutes ≈ 6 meters.

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Answer:

2¼ mph

Step-by-step explanation:

It takes ⅓hour to walk to the library.

⅓ •3 = 1 hour

¾ • 3 = 9/4 = 2¼ miles/hour

Answer:

422.39

Step-by-step explanation:

[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]

use a calculator for the above and round

Answer:

k = 4

Step-by-step explanation:

In the equation: x² - 2x - 24

Replace the x with x + 3

(x+3)² - 2(x+3) - 24

x² + 6x + 9 - 2x - 6 -24

Let's rearrange it

x² + 6x -2x - 24 + 9 - 6

x² - 4x - 21

f(x+3) = x² - 4x - 21

The equivalent value of k from the function is k = -4

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = x² - 2x - 24

Let the second function be represented as B

Now , the value of B is

f ( x + 3 ) = x² - kx - 21

On simplifying , we get

f ( x + 3 ) = ( x + 3 )² - 2 ( x + 3 ) - 24

f ( x + 3 ) = x² + 6x + 9 - 2x - 6 - 24

f ( x + 3 ) = x² + 4x - 21

So , from the equations , we get

-kx = 4x

Divide by -x on both sides , we get

k = -4

Hence , the equation is k = -4

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Answer:

b option is the weight answer I think.

Answer:

Step-by-step explanation:

Let's do this out as best as we can here. Here's the problem:

2 |  3   1   2   -7

___________

The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:

2 |  3   1   2   -7

          6          

    3

Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):

2 |  3   1   2   =7

          6  14      

     3   7

And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:

2 |  3     1     2     -7

            6   14     32

    3      7    16    25

The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees

4a) Given the following

Opposite side = 38cm (side facing the given angle)

Required

Adjacent and hypotenuse side

According to SOH CAH TOA

[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]

Next is to get the adjacent

[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]

Next is to get the missing angle

Since sum of angle in the triangle is 180degrees

32 + 90 + x = 180

122 + x = 180

x = 180 - 122

x = 58degrees

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.

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Answer:

Step-by-step explanation:

Given,

l || m

Therefore,

142° + (3x+8)° = 180° [Since Co-exterior angles]

=> 3x + 8 = 180 - 142

=> 3x + 8 = 38

=> 3x = 38 - 8

=> 3x = 30

[tex] = > x = \frac{30}{3} [/tex]

=> x = 10 (Ans)

Answer:

At most, Liam can only buy lunch for 6 people.

Step-by-step explanation:

It isn't going to be a decimal answer because there can't be half of a person

All you have to do is divide 50 by 8 and round down because you don't want to spend more than 50 dollars.

Writing it mathematically, it would be:

p [tex]\leq[/tex] 6

Their LCM is

70

hope it helps you.

Answer:

Their L.C.M IS

70....

IT IS YOUR ANSWER

Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

vhhg

Step-by-step explanation:

rrgggggggjjhjjhgghghhh

Solution :

For the bigger rectangle

Width of bigger rectangle = W

Length of bigger rectangle, L = 2W

For the smaller rectangle

Width , w = W+4

Length, l = L = 2W

Area, a =120 [tex]m^2[/tex]

Now we know,

Area = length x width

[tex]$a=l \times w$[/tex]

[tex]$120=(2W) \times (W+4)$[/tex]

[tex]$120=2W^2 + 8W$[/tex]

[tex]$2W^2+8W-120=0$[/tex]

[tex]$W^2+4W-60=0$[/tex]

[tex]$(W+10)(W-6) = 0$[/tex]

We get, either [tex]W=-10[/tex]   (rejecting)

                or     [tex]W=6[/tex]

∴ length of the bigger rectangle, [tex]$L=2W $[/tex]

                                                          = 2(6)

                                                           = 12 m

 Length of the smaller rectangle, [tex]$L=2W$[/tex]

                                                            = 2(6)

                                                           = 12 m

Hence, the length of the two gardens is 12 m.                                                            

Answer: a

Step-by-step explanation:

Answer:

V= 562.5 pi cm^3 or approximately 1766.25 cm^3

Step-by-step explanation:

If the diameter is 15, the radius is d/2 = 15/2 = 7.5

The volume of a sphere is

V = 4/3 pi r^3

V = 4/3 ( pi ) (7.5) ^3

V= 562.5 pi

If we use the approximation of 3.14 for pi

V = 1766.25 cm^3

Answer:

Objective Function z

z =  5*x  +  4*y .       to maximize

Step-by-step explanation:

                           eggs             flour

P. Bread    (x)        2                   3

Z. Bread .   (y)       3                  4

Availability .        15                 16

Constraints.

Eggs availability .  15

2*x + 3*y ≤ 15

Flour availability 16 cups

3*x + 4*y ≤16

Objective Function z

z =  5*x  +  4*y .       to maximize

The model:

z =  5*x  +  4*y .       to maximize

Subject to:

2*x + 3*y ≤ 15

3*x + 4*y ≤16

x ≥ 0  y  ≥ 0 .  integers

Answer: C

Step-by-step explanation:

Correct on edg 2020

Answer:

8

Step-by-step explanation:

7 - 2 + 3 = 8

Answer:

9

Step-by-step explanation:

9 / 7 - 2 = 5 + 3 = 8 plus the Dog the man left behind, it would be 9

Answer:

Hello,

Answer A

Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.

Step-by-step explanation:

(a,b,c) is a Pythagorien triple  : c²=a²+b²

and k is a naturel.

[tex](ka)^2+(kb)^2\\\\=k^2*a^2+k^2*b^2\\\\=k^2(a^2+b^2)\\\\=k^2c^2\\\\=(kc)^2\\[/tex]

Answer:

Yes, as long as each number in the Pythagorean Triple is multiplied by the same whole number.

General Formulas and Concepts:

Pre-Algebra

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

In order for it to remain a Pythagorean triple, we must follow the equality rules. To make it the exact same expression, all parts of an equation must be multiplied or divided by the same number. If this is done, then it would also remain a Pythagorean triple, and hence we arrive at our answer.

Answer:

30*sqrt(2)

Step-by-step explanation:

5*sqrt(72)=5*sqrt(36*2)=5*6*sqrt(2)=30*sqrt(2)

Answer:

C.

Step-by-step explanation:

212/4 = 53, so 53/1, or 53 miles are driven every hour.

Answer:

where is the rest of the question??

Step-by-step explanation:

Answer:

The best option would be the second one.

Step-by-step explanation:

This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.