Evaluating function rules
f(x)= -3x^2
f(x)=(1+x)^2​

If we pick a card, roll a die, and find the sum , the different sums possible is 17.

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

If we pick any card and roll a die

The sum possible is

The highest it can be would be  13(card) + 6(die)  =19

the Lowest it can be would be 1(card) + 1 (die)  = 2

So the different sums possible is 19-2 = 17.

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Answer:

541.9

Step-by-step explanation:

Should be, don’t trust me 100%

Answer:

Step-by-step explanation:

A) r = 29

B) The tangents to a circle have same length:

LM = 3*5 + 3 = 18

C) Use the intersecting secants theorem:

Answer:

16.69°

Step-by-step explanation:

Given that,

Height of the building, h = 60 foot

Distance from the base of the building, b = 60 foot

We need to find the angle of elevation must the plane takes off in order to avoid crashing into the building. So,

[tex]\tan\theta=\dfrac{60}{200}\\\\\theta=\tan^{-1}\dfrac{60}{200}\\\\=16.69^{\circ}[/tex]

So, the required angle is 16.69°.

Answer:

(B). 319

Step-by-step explanation:

[tex]\frac{42}{60}[/tex] = [tex]\frac{x}{456}[/tex]

[tex]\frac{7}{10}[/tex] = [tex]\frac{x}{456}[/tex]

x = [tex]\frac{7*456}{10}[/tex] ≈ 319

The best estimate of the number of those parents likely to support the new proposal is 319. So the option is (B) 319.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

Parents of students at a middle school were randomly selected to participate in a survey.

42 out of 60 parents who were surveyed support a proposal to buy new computers.

There are a total of 456 parents with students at the middle-school.

[tex]\dfrac{42}{60} = \dfrac{x}{456} \\\\\\x = \dfrac{42}{60} \times 456\\\\x = \dfrac{7}{10} \times 456\\\\x = 319[/tex]

Therefore, the best estimate of the number of those parents likely to support the new proposal is 319.

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Answer:

x = -1

x + 2 = 1

x = 1 - 2

x = -1

Hope that helps!

-Sabrina

Step-by-step explanation:

9514 1404 393

Answer:

  20

Step-by-step explanation:

The two angles shown are complementary. The corner angles in a rectangle are right angles: 90°.

  (4x -12) +(x +2) = 90

  5x = 100 . . . . . . collect terms, add 10

  x = 20 . . . . . . . . divide by 5

Answer:

y=4x+4

Step-by-step explanation:

It has the biggest slope of the equations of 4, and increases the most.

Answer:

8 - 2n > 18

Step-by-step explanation:

8 less than 2 * a number so represent it with a variable 8 - 2*n

then more than so > 18

Answer:

? = 2    Full Answer: 1/2

Step-by-step explanation:

A regular die has only 6 numbers: 1, 2, 3, 4, 5, & 6.

In those numbers, there are 3 odd numbers, and 3 even numbers. This would mean that the probability of getting an odd number would be 3/6.

But to simplify it, 3/6 ALSO equals 1/2

Answer:

1/2 is the answer

Step-by-step explanation:

A die has 6 possible outcomes: 1, 2, 3, 4, 5, 6

Out of these numbers 3 are odd numbers.

P(Event) = Number of favourable outcomes/ Total number of outcomes

P(odd) = 3/6

           = 1/2

Answer:

y=-5x+6

Step-by-step explanation:

To find your slope (or m value), you must identify 2 points that your line crosses through (I used (1,1) and (0,6). You can either count up and over to the point (0,6) from (1,1), or you can use the formula y2-y1/x2-x1 (it would look like 6-1/0-1). This will give you -5 for your slope.

Your x-intercept (or b value) is 6 because you can see from the graph that that is where your line intercepts y.

I hope this helped :)

Answer: I need a better picture to solve the problem

Step-by-step explanation:

9514 1404 393

Answer:

  x ≈ 7.00

  y ≈ 12.21

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships ...

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

__

Translated to the figure at hand, these are ...

  cos(35°) = 10/y   ⇒   y = 10/cos(35°) ≈ 12.21

  tan(35°) = x/10   ⇒   x = 10·tan(35°) ≈ 7.00

Answer:

145.83 kilómetros.

Step-by-step explanation:

Si un conductor llena su tanque con $600 y recorre 250 kilómetros, para determinar cuántos kilómetros podrá recorrer con $350 de combustible se debe realizar el siguiente cálculo:

600 = 250

350 = X

350 x 250 / 600 = X

87,500 / 600 = X

145.83 = X

Así, con $350 de combustible se podrán recorrer 145.83 kilómetros.

Answer:

Step-by-step explanation:

15-5

a-(-5)

a-(-b)

Answer:

x = 3/2

Step-by-step explanation:

Step (1) :

We should put like term togther:

3x - x = 2 +1

2x = 3

Step (2) :

Divide bothe side by 2:

2x/2 = 3/2

x = 3/2

Answer:

true

Step-by-step explanation:

Answer:

it is one of the bottom 2 I think:)

Answer:

x=50

H=115

Step-by-step explanation:

Answer:

2145

Step-by-step explanation: 55,770/26=2145

Answer:

answer = 2145 per paycheck

Step-by-step explanation:

Answer:

[tex]y=-67.5[cos(\frac{\pi}{15}t)-1][/tex]

Step-by-step explanation:

We can start solving this problem by doing a drawing of London Eye. (See attached picture).

From the picture, we can see that the tourists will start at the lowest point of the trajectory, which means we can make use of a -cos function. So the function will have the following shape:

[tex]y=-Acos(\omega t)+b[/tex]

where:

A=amplitude

[tex]\omega[/tex] = angular speed.

t= time (in minutes)

b= vertical shift.

In this case:

A= radius = 67.5 m

[tex]\omega=2\pi f[/tex]

where the frequency is the number of revolutions it takes every minute, in this case:

[tex]f=\frac{1}{30} rev/min[/tex]

so:

[tex]\omega=2\pi (\frac{1}{30})[/tex]

[tex]\omega=\frac{\pi}{15} rad/min [/tex]

and

b= radius, so

b=A

b=67.5m

so we can now build our equation:

[tex]y=-67.5cos(\frac{\pi}{15} t)+67.5[/tex]

which can be factored to:

[tex]y=-67.5[cos(\frac{\pi}{15}t)-1][/tex]

You can see a graph of what the function looks like in the end on the attached picture.

The required sinusoidal equation is  [tex]y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

Given that,

It has a diameter of 135 meters and makes one revolution (counterclockwise) every 30 minutes.

It is constructed so that the lowest part of the Eye reaches ground level, enabling passengers to simply walk on to, and off of, the ride.

We have to find,

A sinusoidal  which models the height h of the passenger above the ground in meters t minutes after they board the Eye at ground level.

According to the question,

The tourists will start at the lowest point of the trajectory, which means we can make use of a -cos function. So the function will have the following shape:

[tex]y = -Acos(wt) + b[/tex]

Where,  A=amplitude ,  [tex]\omega[/tex] = angular speed, t= time (in minutes) , b= vertical shift.

Then,

[tex]Radius = \dfrac{diameter}{2}\\\\Radius = \dfrac{135}{2}\\\\Radius = 65.5m[/tex]

The frequency is the number of revolutions it takes every minute is determined by the formula is,

[tex]\omega = 2\pi f[/tex]

Where,

[tex]f = \dfrac{1}{30} revolution \ per \ minute[/tex]

Then,

[tex]\omega = 2\pi \times \dfrac{1}{30}\\\\\omega = \dfrac{\pi }{15}\ radian \ per\ minute[/tex]

Here, The sinusoidal equation can be written as;

[tex]y = -67.5cos\dfrac{\pi t}{15} + 67.5\\\\y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

Hence, The required sinusoidal equation is  [tex]y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

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Answer:

The entire trapezoid is 48 units sq

the cut out part is 30

the trapezoid without the cutout is 18

Step-by-step explanation:

The cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

A store is having a sale on trail mix and jelly beans .

Let trail mix = T

and  jelly beans = J

For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18.

i.e

5T + 3J = 18 -------------------------- (1)

For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45.  

i.e

2T + 12J = 45 -------------------------------(2)

Now,

multiplying eq (1) from 4

20T + 12J = 72 -----------------(3)

Solving equation (3) and (2) the equation by elimination method

20T + 12J = 72 -----------------(3)

2T + 12J = 45  -------------------------(2)

subtracting equation (2) from (3)

18T = 27

T = 1.5

substituting the value of T in equation 1

5T + 3J = 18

5*1.5 + 3J = 18

7.5 + 3J = 18

3J = 18 - 7.5

3J = 10.5

J = 3.5

Hence, the cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .

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Answer:

.4

Step-by-step explanation:

52/ /4= 10.4

60/6=10

10.4-10=.4

Michela needs to increase her speed by 0.23 miles/hour to attain her goal.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

She runs 5 miles in 52 minutes.

5 miles in (52/60) hour

In 1 hour → 5(60/52) = 300/52 = 5.769

Her goal was 6 miles in 1 hour.

5.769 + x = 6

x = 0.23 miles/hour

Hence "Michela needs to increase her speed by 0.23 miles/hour to attain her goal".

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